Logical Equivalence And Truth Tables

Step 1: Construct the truth table.
We need to construct a truth table to show that the two expressions are logically equivalent. Consider the columns for $p$ , $q$ , $p%20%5Cleftrightarrow%20q$ , and $(p%20%5Cland%20q)%20%5Clor%20(%5Csim%20p%20%5Cland%20%5Csim%20q)$ . $%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%20%5Chline%20p%20%26%20q%20%26%20p%20%5Cleftrightarrow%20q%20%26%20(p%20%5Cland%20q)%20%5Clor%20(%5Csim%20p%20%5Cland%20%5Csim%20q)%20%5C%5C%20%5Chline%20T%20%26%20T%20%26%20T%20%26%20T%20%5C%5C%20%5Chline%20T%20%26%20F%20%26%20F%20%26%20F%20%5C%5C%20%5Chline%20F%20%26%20T%20%26%20F%20%26%20F%20%5C%5C%20%5Chline%20F%20%26%20F%20%26%20T%20%26%20T%20%5C%5C%20%5Chline%20%5Cend%7Barray%7D$

Step 2: Explanation.
The columns for $p%20%5Cleftrightarrow%20q$ and $(p%20%5Cland%20q)%20%5Clor%20(%5Csim%20p%20%5Cland%20%5Csim%20q)$ are identical, which shows that the two expressions are logically equivalent.

Final Answer: $%5Cboxed%7B%5Ctext%7BThe%20two%20expressions%20are%20logically%20equivalent.%7D%7D$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Logical Equivalence And Truth Tables

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs