Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider statements p and q. p: Milan is hiking. q: Kira is in geometry class. (a) Write each statement below in symbolic form using p and q. (b) Complete the truth table below. Use T for true and F for false. (c) Are Statement 1 and Statement 2 equivalent? Why or why not? Choose the best answer.
Consider statements p and q.
p: Milan is hiking.
q: Kira is in geometry class.
(a) Write each statement below in symbolic form using p and q.
Descriptive form
Symbolic form
q
Statement 1: If Milan is not hiking, then Kira is in geometry class. 0
Ovo
O-0
Statement 2: Kira is not in geometry class and Milan is hiking.
(b) Complete the truth table below. Use T for true and F for false.
You may add more columns. But those added columns will not be graded.
Your answers from part (a) will fill in here.
Statement 1:
Statement 2:
Ovo
F
FT
F F
(c) Are Statement 1 and Statement 2 equivalent? Why or why not? Choose the best answer.
Statement 1 and Statement 2 are equivalent. This is because the truth value of
O Statement 1 is the same as the truth value of Statement 2 for each true-false
combination of p and q.
Statement 1 and Statement 2 are equivalent. This is because the two statements are
made from p and q, and any two statements made from p and q are equivalent.
Statement 1 and Statement 2 are not equivalent. This is because the two statements
are different, and different statements cannot be equivalent.
Statement 1 and Statement 2 are not equivalent. This is because the truth value of
O Statement 1 is different from the truth value of Statement 2 for at least one true-false
combination of p and q.
Transcribed Image Text:Consider statements p and q. p: Milan is hiking. q: Kira is in geometry class. (a) Write each statement below in symbolic form using p and q. Descriptive form Symbolic form q Statement 1: If Milan is not hiking, then Kira is in geometry class. 0 Ovo O-0 Statement 2: Kira is not in geometry class and Milan is hiking. (b) Complete the truth table below. Use T for true and F for false. You may add more columns. But those added columns will not be graded. Your answers from part (a) will fill in here. Statement 1: Statement 2: Ovo F FT F F (c) Are Statement 1 and Statement 2 equivalent? Why or why not? Choose the best answer. Statement 1 and Statement 2 are equivalent. This is because the truth value of O Statement 1 is the same as the truth value of Statement 2 for each true-false combination of p and q. Statement 1 and Statement 2 are equivalent. This is because the two statements are made from p and q, and any two statements made from p and q are equivalent. Statement 1 and Statement 2 are not equivalent. This is because the two statements are different, and different statements cannot be equivalent. Statement 1 and Statement 2 are not equivalent. This is because the truth value of O Statement 1 is different from the truth value of Statement 2 for at least one true-false combination of p and q.
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