Question

Consider statements and .p : The SUV is on the road.q : A layer of snow is below us.(a)Write each statement below in symbolic form using and .Statement : It is false that "a layer of snow is not below us and the SUV is on the road."Statement : If the SUV is on the road, then a layer of snow is below us.(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. statement 1 statement 2TTTFFTFF(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 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 Statement 1 is different from the truth value of Statement 2 for at least one true-false combination of p and q.

Answer 1

Given the statements:

`\begin{gathered} p\colon The\text{ SUV }is\text{ on the road} \\ q\colon A\text{ layer of snow is before us} \end{gathered}`

The symbolic form of the statements below are:

statement 1: It is false that a layer of snow is not below us and the SUV is on the road

`\approx q\Lambda p`

statement 2: If the SUV is on the road, then a layer of snow is before us