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.

The statement is a tautology

Step-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 , which is compound by these statements:

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:

by the logical equivalence involving conditional statement.

by De Morgan's Law

by the Double negation law

by the Idempotent law

by Associative law

by Negation law

by Domination law

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.