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Analyze and answer the following statements. 1. State whether each bi-conditional is true or false. a. x> 7 if and only if x > 6 b. x+5 > 7 if and only if x > 2

Analyze and answer the following statements. 1. State whether each bi-conditional is true or false. a. x> 7 if and only if x > 6 b. x+5 > 7 if and only if x > 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Analyze and answer the following statements. 1. State whether each bi-conditional is true or false. a. x> 7 if and only if x > 6 b. x+ 5 > 7 if and only if > 2 2. Use p, q, and r as defined in Example 6. Write the following symbolic statements in words: a. p A ^~r b. ~q 4 ^r 3. Write the negation of each conditional statement. a. If I finish the report, I will go to the concert. b. If the square of n is 25, then n is 5 or – 5. 4. Write each of the following in its equivalent disjunctive form. a. If I don't move to Georgia, I will live in Houston. b. If the number is divisible by 2, then the number is even. 5. Construct a truth table for [p ^ (p → q)] – q. 6. Determine the truth value of each of the following conditional statements. a. If 4 > 3, then 2 +5 = 6 b. If 5 > 9, the 4 > 9 c. If Tuesday follows Monday, then April follows march. 7. Identify the antecedent and consequent in each of the following conditional statements. a. If I study for at least 6 hours, then I will get an A on the test. b. If I get the job, I will buy a new car. c. If you can dream it, you can do it. d.
Transcribed Image Text:Analyze and answer the following statements. 1. State whether each bi-conditional is true or false. a. x> 7 if and only if x > 6 b. x+ 5 > 7 if and only if > 2 2. Use p, q, and r as defined in Example 6. Write the following symbolic statements in words: a. p A ^~r b. ~q 4 ^r 3. Write the negation of each conditional statement. a. If I finish the report, I will go to the concert. b. If the square of n is 25, then n is 5 or – 5. 4. Write each of the following in its equivalent disjunctive form. a. If I don't move to Georgia, I will live in Houston. b. If the number is divisible by 2, then the number is even. 5. Construct a truth table for [p ^ (p → q)] – q. 6. Determine the truth value of each of the following conditional statements. a. If 4 > 3, then 2 +5 = 6 b. If 5 > 9, the 4 > 9 c. If Tuesday follows Monday, then April follows march. 7. Identify the antecedent and consequent in each of the following conditional statements. a. If I study for at least 6 hours, then I will get an A on the test. b. If I get the job, I will buy a new car. c. If you can dream it, you can do it. d.
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