Question

Please help 20 points!

What is the truth value for the following conditional statement?
1.)
p: true
q: true

p → q

2.)
p: true
q: false

p → q

3.)
p: false
q: false

p → q

4.)
p: true
q: true

∼p → q

Answer 1

The truth value for the following conditional i.e., conjunction statement P is false and Q is true is False.

Answer 2

• 1) True
• 2) False
• 3) True
• 4) True

Explanation:

This conditional statement:

• If a its true, then b its true.

Has a truth value of true if:

• both a and b are true.
• a its false, besides the truth value of b

And has a truth value of false, if

• a is true and b is false

Then, for this statements:

1. p -> q

As both p and q are true, then, this statement is true.

2. p -> q

As p is true and q is false, this statement is false.

3. p->q

As p is false, this statement is true, no matter the truth value of q.

4. ∼p -> q

∼p its the negation of p. if p is true, then ∼p is false. And this statement is true, no matter the truth value of q.