What is equivalent to P iff Q?

What is equivalent to P iff Q?

The proposition p ↔ q, read “p if and only if q”, is called bicon- ditional. It is true precisely when p and q have the same truth value, i.e., they are both true or both false. Note that that two propositions A and B are logically equivalent precisely when A ↔ B is a tautology.

Is P Q and Q P equivalent?

Two statement forms are logically equivalent if, and only if, their resulting truth tables are identical for each variation of statement variables. p q and q p have the same truth values, so they are logically equivalent.

What is the negation of P iff Q?

The negation of p ∧ q asserts “it is not the case that p and q are both true”. Thus, ¬(p ∧ q) is true exactly when one or both of p and q is false, that is, when ¬p ∨ ¬q is true.

What does P only if Q mean?

Only if introduces a necessary condition: P only if Q means that the truth of Q is necessary, or required, in order for P to be true. That is, P only if Q rules out just one possibility: that P is true and Q is false.

Is P → Q → [( P → Q → Q a tautology Why or why not?

(p → q) and (q ∨ ¬p) are logically equivalent. So (p → q) ↔ (q ∨ ¬p) is a tautology.

Is P -> Q equivalent to Q -> p?

Converse: Suppose a conditional statement of the form “If p then q” is given. The converse is “If q then p.” Symbolically, the converse of p q is q p. A conditional statement is not logically equivalent to its converse.

What is the truth value of the compound proposition P → Q ↔ P if P is false and Q is true?

Tautologies and Contradictions

How do you negate p implies q?

The negation of “P and Q” is “not-P or not-Q”. The negation of “P or Q” is “not-P and not-Q”.

Is P ↔ Q equivalent to P ↔ Q justify?

Two propositions p and q are logically equivalent if their truth tables are the same. Namely, p and q are logically equivalent if p ↔ q is a tautology.