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Can someone share the answer of this problem and explain in words how you got that? It's about "and" and "or" statements.?
If p, q, and r are statements and p is true, then the statement (p ∧ q) --> (p ∨ r) is...
True
False
True only if q is true
False only if q is true.
(I know the answer already. I just don't know why it is correct.)
1 Answer
- MewtwoLv 56 years ago
The statement q must be true. A conditional statement is true if both the premises and the conclusion are true. Since an OR statement is true whenever its premises are true, regardless of the conclusion, and an AND statement is true only if both parts of the statement is true; then the conditional will be true as long as both the AND and OR statements are true. Since p is true, the OR statement is true and we need only focus on the AND statement. This is what requires that q be a true statement.
