Answer to Question #125829 in Discrete Mathematics for EFTY

Question

Determine whether the following preposition is tautology, contradiction or contingency and explain the answer by your own words.

(p↔q ) ⊕ ¬(q→p) 

Answer 1

If $p = False,\; q = True$

then $(p \leftrightarrow q) = False,\; (q \rightarrow p ) = False$

so $(p \leftrightarrow q) \; \oplus \; \neg(q \rightarrow p) = False \; \oplus \; \neg False = True$

The following preposition is not a contradiction.

If $p = True,\; q = False$

then $(p \leftrightarrow q) = False,\; (q \rightarrow p ) = True$

so $(p \leftrightarrow q) \; \oplus \; \neg(q \rightarrow p) = False \; \oplus \; \neg True = False$

The following preposition is not a tautology.

It means that the following preposition is a contingency.