Question

See attached I wasn’t able to write all the characters:Suppose r and p are true, and the statements s and t are false. Indicate the truth value of each statement. Do not construct a truth table

Answer 1

r and p = true

s and t = false

The logical expression is given by

$(p\wedge t)\leftrightarrow(p\rightarrow s)$

Let us solve the above expression.

(p ∧ t) means p and t

(p ∧ t) is true if p and t both are true.

But we know that both p and t are not true since t is false.

So, (p ∧ t) is false.

(p -> s) means p implies s

(p -> s) is true if p is false or s is true.

But we know that p is true and s is false.

This means that (p -> s) is false.

Finally,

↔ means equivalent

(p ∧ t) ↔ (p -> s) is true if both are true or both are false.

We know that (p ∧ t) is false and (p -> s) is false

So, (p ∧ t) ↔ (p -> s) is true since both of them are false.