Question

determine the truth values of p, q, and r that would make the statement false. Explain your reasoning. p→(q∨~r)   ​

Answer 1

Answers:

• p = true
• q = false
• r = true

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Step-by-step explanation:

For a conditional to be false, the antecedent must be true and the conclusion must be false. So the format is (true) --> (false) for the overall conditional to be false.

Since the antecedent must be true, this means p = true. We can shorten this to say p = T, where T stands for "true".

Now we must make (q v ~r) be false.

This is only possible if both pieces q and ~r are false. An "or" statement, aka disjunction, is true if either piece is true; otherwise it's false.

So q = F, where F stands for "false" and ~r = F as well.

If ~r = F, then r = T. Recall the squiggly line or tilde is basically the negation operator. It does the opposite of the statement.