Question

1. if the truth values of both ( p ) and ( q ) are ( f ), then which of the following is a valid statement?

a. the truth value of ( p \to q ) is ( f ).
b. the truth value of ( p \to q ) is ( t ).
c. the truth value of ( p \to q ) could be either ( t ) or ( f ).
d. the truth value of ( p \to q ) cannot be determined without knowing what ( p ) and ( q ) represent.

1. does ( \triangle abc ) appear to be the same size and shape as ( \triangle xyz )? explain.

a. yes; ( \triangle abc ) maps onto ( \triangle xyz ) with a translation and a rotation.
b. yes; ( \triangle abc ) maps onto ( \triangle xyz ) with a translation and a reflection.
c. yes; ( \triangle abc ) maps onto ( \triangle xyz ) with a rotation and a reflection.
d. no; the triangles are different sizes.

Explanation:

Step1: Recall the truth - table for implication

The truth - table for \(p
ightarrow q\) is as follows:

\(p\)

\(q\)

\(p

ightarrow q\) |

\(T\)	\(T\)	\(T\)
\(T\)	\(F\)	\(F\)
\(F\)	\(T\)	\(T\)
\(F\)	\(F\)	\(T\)

Step2: Substitute \(p = F\) and \(q = F\) into the truth - table

When \(p = F\) (False) and \(q = F\) (False), from the truth - table of \(p
ightarrow q\), we can see that \(p
ightarrow q\) is \(T\) (True).

Answer:

B. The truth value of \(p
ightarrow q\) is \(T\).