1301 3.1 Statements & Logical Connectives UTA
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Apr 3, 2024
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Student:., ; i Date: 03/25/24 Legault, Juan Silva, Math Dept Course: 2242-MATH-1301-502- CONTEMPORARY MATH Connectives Fill in the blank. A sentence that can be judged either true or false is called a(n) A sentence that can be judged either true or false is called a(n) statement. 2. Fillin the blank. A statement that consists of two or more simple statements is called a statement. A statement that consists of two or more simple statements is called a compound statement. 3. Select the correct choices that complete the sentences below. a) The negation is symbolized by ~ and is read " . b) The conjunction is symbolized by A and is read " c¢) The disjunction is symbolized by Vv and is read " N a) The negation is symbolized by ~ and is read "not." b) The conjunction is symbolized by A and is read "and." c) The disjunction is symbolized by v and is read “or." @Decide whether the following statement is compound. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. Julie's sister likes swimming for fun. Is the statement a compound statement? ¥ No Yes Assignment: 3.1 Statements and Logical If the statement is compound, is it a negation, conjunction, disjunction, conditional, or biconditional? Choose the correct answer below. * A. conditional, — B. negation, ~ ¥ C. The statement is simple. : D. disjunction, Vv E. conjunction, A > F. biconditional, <
5. Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. Statement: A triangle is isosceles if and only if it has two sides that are the same length. Is the above statement simple or compound? A. The statement is a simple statement because it has only one idea. :¥B. The statement is a compound statement because it combines two or more simple statements. C. The statement is a compound statement because it has only one idea. 7.+ D. The statement is a simple statement because it combines two or more simple statements. If the statement is compound, is it a negation, conjunction, disjunction, conditional, or biconditional? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. " A. The statement is a disjunction. It is represented by the symbol - B. The statement is a conditional. It is represented by the symbol »* €. The statement is a conjunction. It is represented by the symbol © D. The statement is a negation. It is represented by the symbol WE, The statement is a biconditional. It is represented by the symbol « : F. The statement is simple. 6. Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. Statement: Dave likes to play football and he likes to play soccer. Is the above statement simple or compound? * A, The statement is a simple statement because it combines two or more simple statements. . B. The statement is a simple statement because it has only one idea. .- C. The statement is a compound statement because it has only one idea. ¥D. The statement is a compound statement because it combines two or more simple statements. If the statement is compound, is it a negation, conjunction, disjunction, conditional, or biconditional? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. YA The statement is a conjunction. It is represented by the symbol A - The statement is a disjunction. It is represented by the symbol B ©: C. The statement is a biconditional. It is represented by the symbol D * + D. The statement is a conditional. It is represented by the symbol W ~ E. The statement is a negation. It is represented by the symbol_ M\t«/ o X I+ F. The statement is simple. bV / ~ ve V \
7. Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. Statement: If it snows tonight, then there will be no school tomorrow. Is the above statement simple or compound? ¥ A. The statement is a compound statement because it combines two or more simple statements. * + B. The statement is a simple statement because it combines two or more simple statements. C. The statement is a simple statement because it has only one idea. D. The statement is a compound statement because it has only one idea. If the statement is compound, is it a negation, conjunction, disjunction, conditional, or biconditional? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. + A The statement is a negation. It is represented by the symbol vB. The statement is a conditional. It is represented by the symbol - - C. The statement is a biconditional. It is represented by the symbol D. The statementis a conjunction. It is represented by the symbol E. The statement is a disjunction. It is represented by the symbol F. The statement is simple. Write the negation.of the statement. All pigs fly. Choose the correct answer below. v <:_,._/ A. Some pigs do not fly. B. Some pigs fly. C. No pigs fly. . D. All pigs do not fly. _ ./ 9. Write the negation of the statement. Some turtles do not have claws. Choose the correct answer below. Y A. All turtles have claws. - - B. Not all turtles have claws, C. Some turtles have claws. AR " D. No turtles have claws. ——— s— @ Let p and q represent the following statements. p: The fire is burning. q: The key of C has three flats. Express the following statement symbolically. The fire is not burning. Symbolically, the statement is ~p
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(:1. pWrite the statement in symbolic form. Let p and q represent the following statements. p: The crowd is going wild. q: The band is playing an encore. The band is not playing an encore or the crowd is not going wild. The statement in symbolic form is ~qv~p i 12.'>Let p and q represent the following simple statements. p: This is a turtle. q: This is a reptile. Write the following compound statement in symbolic form. If this is not a turtle, then this is not a reptile. The compound statement written in symbolic form is ~p—~q 13. Let p and q represent the following statements. p: The stove is hot. g: The soup is cold. Write the following statement in its symbolic form. The stove is not hot, but the soup is cold. The statement "The stove is not hot, but the soup is cold." is written ~pAq 14. Let p and q represent the following statements. p: The play is boring. q: The actors are talented. Write the following compound statement in its symbolic form. The actors are not talented if and only if the play is boring. The statement "The actors are not talented if and only if the play is boring.” is written ~qep . » J =gl = ¥ @ Write the statement in symbolic form. Let p and q represent the following statements. \ /7 & '\ '/, p: The chili is spicy. AP | q: The sour cream is cold. / A It is false that the chili is spicy or the sour cream is cold. Choose the correct answer below. AN R v i A. ~(pAQ)
16. 17. 18. Let p represent the following statement. p: The largest organ in the human body is skin. Express the symbolic statement ~p in words. In words, the symbolic statement ~p is which of the following? A. The largest organ in the human body is the heart. B. The smallest organ in the human body is skin. C. The largest organ in the human body may be the skin. D. The largest organ in the human body is not skin. Let p and g represent the following simple statements. p: The taxes are high. q: The chair is broken. Write the symbolic statement ~ (qvp) in words. Choose the correct sentence below. The chair is not broken or the taxes are not high. It is not true that the chair is broken and the taxes are high. ¥ ltis not true that the chair is broken or the taxes are high. The chair is not broken or the taxes are high. Let p and q represent the following simple statements. p: It is Tuesday. q: The taxes are high. Write the symbolic statement ~ (pAq) in words. Choose the correct sentence below. Itis not Tuesday and the taxes are not high. ¥ Jtis not true that it is Tuesday and the taxes are high. It is not true that it is Tuesday or the taxes are high. It is not true that it is not Tuesday and the taxes are not high. ’1’9. Let p, q, and r represent the following simple statements. p: It is snowing outside. q: The chair is broken. r: | work hard. Write the following compound statement in its symbolic form. It is snowing outside and the chair is broken, or | work hard. The symbolic form is (pAg)vr
20";‘ Let p, g, and r represent the following statements. -’ p: | work hard. q: | get a raise. r: The job pays well. Write the following compound statement in its symbolic form. If the job pays well and | get a raise, then | work hard. The symbolic formis (rAqQ)—p 21. Letp, q, and r represent the following simple statements. p: | study. g: It is snowing outside. r: This is an octopus. Write the symbolic statement in words. PVQ A ~r Choose the correct answer below. ¥ A. |study orit is snowing outside, and this is not an octopus. B. Itis snowing outside and | study, or this is not an octopus. C. |study, and it is snowing outside or this is not an octopus. D. ltis snowing outside, or | study and this is not an octopus. 22. Letp, q, and r represent the following simple statements. p: | eat bananas. q: The stove is hot. r: It is Tuesday. Write the symbolic statement in words. ~pA(QVr) Choose the correct answer below. A. The stove is not hot, or | eat bananas and it is Tuesday. " B. The stove is not hot and | eat bananas, or it is Tuesday. ¥ C. |do not eat bananas, and the stove is hot or it is Tuesday. D. | do not eat bananas or the stove is hot, and it is Tuesday. 23. Letp, q, and r represent the following simple statements. p: It is snowing outside. q: It is Tuesday. r: The taxes are high. Write the symbolic statement in words. ~r=(q AP Choose the correct answer below. If the taxes are high then it is Tuesday, and it is snowing outside. ¥ B. If the taxes are not high, then it is Tuesday and it is snowing outside. C. If the taxes are high then it is not Tuesday, and it is not snowing outside. D. If the taxes are not high, then it is not Tuesday and it is snowing outside.
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24, 25, 26. 27. Let p, q, and r represent the following simple statements. p: This is an octopus. g: The taxes are high. r: | work hard. Write the symbolic statement in words. (@—=rnAp Choose the correct answer below. A. If the taxes are high, then | work hard and this is an octopus. B. If this is an octopus, then | work hard or the taxes are high. If the taxes are high then | work hard, and this is an octopus. D. If this is an octopus then the taxes are high, or | work hard. Let p, g, and r represent the following simple statements. p: It is Tuesday. q: The taxes are high. r: The chair is broken. Write the symbolic statement in words. ({@ep)Ar Choose the correct answer below. It is Tuesday if and only if the taxes are high, or the chair is broken. B. Itis Tuesday, if and only if the chair is broken or the taxes are high. C. The taxes are high if and only if it is Tuesday, and the chair is broken. D. The taxes are high, if and only if the chair is broken and it is Tuesday. A restaurant dinner menu includes the following statement. All dinners are served with a choice of: salad or rice, and onion rings or chicken, and broccoli or asparagus. Is it permissible to select a single dinner with salad, rice, and asparagus? If not, explain why. Choose the correct answer below. A. ltis not permissible because both rice and asparagus cannot be selected at the same time. B. lItis not permissible because both salad and asparagus cannot be selected at the same time. C. ltis permissible. D. lItis not permissible because both salad and rice cannot be selected at the same time. A restaurant dinner menu includes the following statement. All dinners are served with a choice of: salad or soup, and chicken or pasta, and peas or broccoli. Is it permissible to select a single dinner with salad, chicken, pasta, and broccoli? If not, explain why. Choose the correct answer below. Y A. Itis not permissible because both chicken and pasta cannot be selected at the same time. B. ltis not permissible because both pasta and broccoli cannot be selected at the same time. C. ltis permissible. D. Itis not permissible because both salad and chicken cannot be selected at the same time. ——
28. 29. For the statement below, perform the following. a. Write the statement symbolically by using parentheses. b. Determine whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. Statement: | did not buy the watch in the city and | spent $100. a. Which symbolic statement best represents the written statement? p: | bought the watch in the city. q: | paid $100. A. pVv ~q i"B. pA ~q i C. ~pVaQq ‘@D, ~pAg b. Is the statement found in part (a) a negation, conjunction, disjunction, conditional, or biconditional? A. Dbiconditional ¥ B. conjunction C. conditional D. negation E. disjunction For the statement below, perform the following. a. Write the statement symbolically by using parentheses. b. Determine whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. Statement: It is false that if you eat at a restaurant then you will not order a dessert. a. Which symboalic statement best represents the written statement? p: You eat at the restaurant. q: You will order a dessert. LA pe ~q L.B. p— ~q Ye. ~(p— ~q) D ~(po ~q) b. Is the statement found in part (a) a negation, conjunction, disjunction, conditional, or biconditional? A. conditional ¥ B. negation C. biconditional D. disjunction E. conjunction
30. 31. For the statement below, write the statement symbolically using parentheses and determine whether it is a negation, conjunction, disjunction, conditional, or biconditional. Statement: If | have cash or | have a credit card, then | can buy groceries. a. Which symbolic statement best represents the written statement? p: | have cash. q: | have a credit card. r: | can buy groceries. AL (pvQer 3B (pAQ)—T G (~pvQg)—r ¥D. pvq)—or b. Is the statement found in part (a) a negation, conjunction, disjunction, conditional, or biconditional? ¥ A. conditional ¢ B. disjunction C. negation -+ D. conjunction E biconditional For the statement below, perform the following. a. Write the statement symbolically by using parentheses. b. Determine whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. Statement: You may go on the trip, if and only if you do not have school or you have a snow day tomorrow. a. Which symbolic statement best represents the written statement? p: You may go on the trip. g: You have school. r: You have a snow day tomorrow ‘A p=(~qvr) B. (p—> ~q)vr MC. po(~qvrn) D (pe ~q)vr b. Is the statement in part (a) a negation, conjunction, disjunction, conditional, or biconditional? A. disjunction B. negation C. conditional D. biconditional E. conjunction
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32. For the statement below, write the statement symbolically using parentheses and determine whether it is a negation, conjunction, disjunction, conditional, or biconditional, Statement: | will not pass the exam if and only if | do not study weli, or the exam is not hard. a. Which symbolic statement best represents the written statement? p: | will pass the exam. q: | study well. r: The exam is hard. CEAL {~pe ~q)A ~T 7iB. (~pe ~q)Vr G (~po ~q)V ~r MD. (~pe ~q)V ~r b. Is the statement in part (a) a negation, conjunction, disjunction, conditional, or biconditional ? biconditional negation conditional conjunction moow?» disjunction Caont '\ ol = Condw PR