Show that (-91(pvp)) +n is a tautology (i.e. (91(pvp)) +7=T). (a) (3 points) Show the equivalence using truth tables (b) (4 points) Show the equivalence by establishing a sequence of equiv- alences. You can only use the equivalences in Table 6 and the first equivalence in Table 7. Show your work by annotating every step.

Answer:The statement [tex](\lnot q \land(p\lor p))\rightarrow \lnot q[/tex] is a tautologyStep-by-step explanation:A tautology is a statement that is true for every assignment of truth values to its simple components.a) A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.We have the statement [tex](\lnot q \land(p\lor p))\rightarrow \lnot q[/tex], which is compound by these statements:[tex]\lnot q[/tex][tex]p\lor p[/tex][tex]\lnot q \land(p\lor p)[/tex]and we are going to use these simple statements to build the truth table.The last column contains only true values. Therefore, the statement is a tautology.b) We are going to use the table of logical equivalences as follows:[tex](\lnot q \land(p\lor p))\rightarrow \lnot q \equiv[/tex][tex]\equiv \lnot(\lnot q \land(p\lor p)) \lor \lnot q[/tex] by the logical equivalence involving conditional statement.[tex]\equiv \lnot(\lnot q) \lor \lnot(p\lor p) \lor \lnot q[/tex] by De Morgan's Law[tex]\equiv q \lor \lnot(p\lor p) \lor \lnot q[/tex] by the Double negation law[tex]\equiv q \lor \lnot p \lor \lnot q[/tex] by the Idempotent law[tex]\equiv (q \lor \lnot q)\lor \lnot p[/tex] by Associative law[tex]\equiv T\lor \lnot p[/tex] by Negation law[tex]\equiv T[/tex] by Domination law