Consider statements P and q. p: Melissa is practicing baseball. q: Hans is playing piano. (a) Write each statement below in symbolic form using P and q. Descriptive form Symbolic form Statement 1 : If Melissa is practicing baseball, then Hans is not playing piano. ロvロ ローロ ローロ Statement 2: It is false that "Melissa is practicing baseball and Hans is playing piano." U (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: T OvO ローロ FF 中 up (c) Are Statement 1 and Statement 2 eguivalent? 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 9. Statement I and Statement 2 are equivalent. This is because the two statements are made from p and 9, and any two statements made from P and 9 are equivalent. Statement I 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 9.
Consider statements P and q. p: Melissa is practicing baseball. q: Hans is playing piano. (a) Write each statement below in symbolic form using P and q. Descriptive form Symbolic form Statement 1 : If Melissa is practicing baseball, then Hans is not playing piano. ロvロ ローロ ローロ Statement 2: It is false that "Melissa is practicing baseball and Hans is playing piano." U (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: T OvO ローロ FF 中 up (c) Are Statement 1 and Statement 2 eguivalent? 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 9. Statement I and Statement 2 are equivalent. This is because the two statements are made from p and 9, and any two statements made from P and 9 are equivalent. Statement I 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 9.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:Consider statements P and q.
p: Melissa is practicing baseball.
q: Hans is playing piano.
(a) Write each statement below in symbolic form using P and q.
Descriptive form
Symbolic form
Statement 1 : If Melissa is practicing baseball, then Hans is not playing piano.
~ロ
ロvロ
ローロ
Statement 2: It is false that "Melissa is practicing baseball and Hans is playing piano." U
(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
0.
T
OvO
F
ローロ
FF
(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 9.
Statement 1 and Statement 2 are equivalent. This is because the two statements are
made from p and 9, and any two statements made from P and 9 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 9.
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