Answer to Question #50190 in Discrete Mathematics for Sajid Mehmood

Question

without using truth table prove that
[(p˅q)˄(p→r)˄(q→r)]→r is a tautology.

Answer 1

Firstnotice what this says: if one of two things are true (either p or q) and each
implies a third statement (r), then r must be true. Clearly this is tautology,
since if p is true we have p→r, hence r, and similarly if q is true.