Equivalences Show that (p and q) rightarrow q is a tautology (i.e. (p and q) rig

Question

Equivalences Show that (p and q) rightarrow q is a tautology (i.e. (p and q) rightarrow q Congruent T). (a) Show the equivalence using truth tables (b) Show the equivalence by establishing a sequence of equivalences. You can only use the equivalences in Table 6 and the first equivalence in Table 7. Show your work by annotating every step. Show that (p rightarrow q) and (p rightarrow r) Congruent p rightarrow (q and r) (a) Show the equivalence using truth tables (b) Show the equivalence by establishing a sequence of equivalences. You can only use the equivalences in Table 6 and the first equivalence in Table 7. Show your work by annotating every step.

Explanation / Answer

p q p^q p^q->q
T T T T
T F F T
F T F T
F F F T

From this truth table we can see that p^q->q is a tautology;

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