Complete the truth table and determine whether or not ∼(p∧q

Homeworklib Q&A #1085 - Complete the truth table and determine whether or not  ∼(p∧q

Complete the truth table and determine whether or not

∼(p∧q)≡∼p∨∼q

Are the two statements equivalent?
A. No, the rows are not identical.
B. Yes, the columns are identical.
C. No, the columns are not identical.
D. Yes, the rows are identical.

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Homeworklib Your Answer

1 General guidance

 The answer provided below has been developed in a clear step by step manner.

2 Step By Step

Step 1

 Consider the given statements:

∼(p∧q)≡∼p∨∼q

 

Explanation

 

• p ⋀ q is true only if both p and q are true, otherwise false.
• p ⋁ q is false only if both p and q are false, otherwise true.
• p → q is false only when p is true and q is false, otherwise true.
• p ↔ q is true if both p and q are true and also both are false, otherwise false.
• If p is true then ¬p false and vice versa

 

Step 2

B. Yes, the columns are identical. (see columns with border)

therefore given statements are equivalent.

 

 

Explanation

Please refer to solution in this step.

3 Answer

 

B. Yes, the columns are identical. (see columns with border)

therefore given statements are equivalent.

 

 

Now construct the truth table of given statement: