Question

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 1

techno never dies

Explanation:

techno never dies

Answer 2

The statement
`(\lnot q \land(p\lor p))\rightarrow \lnot q` is a tautology

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
`(\lnot q \land(p\lor p))\rightarrow \lnot q`, which is compound by these statements:

• 
  `\lnot q`
• 
  `p\lor p`
• 
  `\lnot q \land(p\lor p)`

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:

`(\lnot q \land(p\lor p))\rightarrow \lnot q \equiv`

`\equiv \lnot(\lnot q \land(p\lor p)) \lor \lnot q` by the logical equivalence involving conditional statement.

`\equiv \lnot(\lnot q) \lor \lnot(p\lor p) \lor \lnot q` by De Morgan's Law

`\equiv q \lor \lnot(p\lor p) \lor \lnot q` by the Double negation law

`\equiv q \lor \lnot p \lor \lnot q` by the Idempotent law

`\equiv (q \lor \lnot q)\lor \lnot p` by Associative law

`\equiv T\lor \lnot p` by Negation law

`\equiv T` by Domination law