Consider statements p and q. p: The truck is on the road. q: A valley is below us. (a) Write each statement below in symbolic form using p and q. Symbolic Descriptive form form OvO Statement 1: If the truck is on the road, then a valley is below us. Statement 2: If a valley is not below us, then the truck is not on the road. (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 T F O-0 F F F (c) Are Statement 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 fromp 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.
Consider statements p and q. p: The truck is on the road. q: A valley is below us. (a) Write each statement below in symbolic form using p and q. Symbolic Descriptive form form OvO Statement 1: If the truck is on the road, then a valley is below us. Statement 2: If a valley is not below us, then the truck is not on the road. (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 T F O-0 F F F (c) Are Statement 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 fromp 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Consider statements p and q.
p: The truck is on the road.
q: A valley is below us.
(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.
Transcribed Image Text:Consider statements p and q.
p: The truck is on the road.
q: A valley is below us.
(a) Write each statement below in symbolic form using p and q.
Symbolic
Descriptive form
form
OvO
Statement 1: If the truck is on the road, then a valley is below us.
Statement 2: If a valley is not below us, then the truck is not on the
road.
(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
O-0
F
F
F
?
(c) Are Statement
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 fromp 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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