
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:Consider statements p and q.
p: The path is in the park.
q: A balloon is above us.
(a) Write each statement below in symbolic form using p and q.
Descriptive form
Symbolic form
q
Statement 1: If the path is in the park, then a balloon is not above us.
OvO
O-0
Statement 2: It is false that "the path is in the park or a balloon is above us." I
(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:||
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Transcribed Image Text: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.
Sa
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