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Simplify ¬¬n∧t to n:

(a) Apply the next logical law from the right.
(b) Identify the equivalent expression using the laws of logic.
(c) Simplify the expression using De Morgan's laws.
(d) Determine the truth value of the expression.

1 Answer

4 votes

Final answer:

The expression ¬¬n∧t can be simplified to ¬(¬n∨¬t) using De Morgan's laws.

Step-by-step explanation:

The given expression is ¬¬n∧t. We need to simplify this expression to n.

(a) Apply the next logical law from the right: Starting from the right, we have t. So, we can rewrite the expression as ¬¬n∧t = ¬¬n∧t.

(b) Identify the equivalent expression using the laws of logic: The expression ¬¬n∧t is equivalent to n∧t by the Double Negation Law (¬¬n = n).

(c) Simplify the expression using De Morgan's laws: We can rewrite n∧t as ¬(¬n∨¬t) using De Morgan's Law. So, the simplified expression is ¬(¬n∨¬t).

(d) Determine the truth value of the expression: The truth value of the expression ¬(¬n∨¬t) depends on the values of n and t. If both n and t are true, then the expression is false. Otherwise, the expression is true.

User Dilip Lilaramani
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