$p\rightarrow (q\rightarrow p)\equiv \lnot p\lor (q\rightarrow p) \equiv \lnot p\lor (\lnot q\lor p) \equiv (p\lor \lnot p) \lor \lnot q \equiv T \lor \lnot q \equiv T$

Step-by-step explanation:

We have the following statement:

$p\rightarrow (q\rightarrow p)$

To reduce the statement to a tautology we need to use the table of logical equivalences as follows:

$p\rightarrow (q\rightarrow p)\equiv$

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

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

$\equiv (p\lor \lnot p) \lor \lnot q$ by the Associative law.

$\equiv T \lor \lnot q$ by the Negation law.

$\equiv T$ by the Domination law.

7 0

3 years ago

How do you do zero pairs

Nataliya [291]

Zero pairs are basically 2 numbers that add up to zero like -1 +1 = 0 they cancel each other out. By assigning tiles to represent each number, you can cancel out the zero pairs and the remaining tiles will represent the sum or difference of the numbers.

5 0

3 years ago

A high school coach wants to buy new shirts for the 25 members of the track team. The coach must spend less than $300 on the shi

aksik [14]

25 less than or equal too 300,not really enough information

3 0

3 years ago