Question

Use the laws of propositional logic to prove the following:

Answer 1

Answer:

I attached the answer in the picture

Explanation:

Logical True and Logical False

These are kinda strange operations. Logical true always results in True and logical false always results in False no matter the premise. These operations are often referred to as “always true” and “always false”.

Binary Operators

Binary operators require two propositions. We’ll use p and q as our sample propositions.

Negation

The negation operator is commonly represented by a tilde (~) or ¬ symbol. It negates, or switches, something’s truth value.

We can show this relationship in a truth table. A truth table is a way of organizing information to list out all possible scenarios.

AND

The AND operator (symbolically: ∧) also known as logical conjunction requires both p and q to be True for the result to be True. All other cases result in False. This is logically the same as the intersection of two sets in a Venn Diagram.

Implication

Logical implication (symbolically: p → q), also known as “if-then”, results True in all cases except the case T → F. Since this can be a little tricky to remember, it can be helpful to note that this is logically equivalent to ¬p ∨ q (read: not p or q)*.