Question

Use truth tables to verify these equivalences

Short answer

The given equivalences can be verified with the help oftruth tables.Prepare truth table for every logical expression and also take different values of such as all the possible combinations of T and F to check the result for verification of specified equivalences.

Step-by-step solution

Definition of Truth Table

A logic gate truth tabledepicts each feasible input sequence to the gate or circuit, as well as the resulting output based on the combination of these inputs.

Verification of Logical Equivalences using Truth Table

(a)$\text{p}\wedge \text{T}\equiv \text{p}$

Prepare a truth table for the verification of $\text{p}\wedge \text{T}\equiv \text{p}$

Truth Table

From the truth table, it is true that $\text{p}\wedge \text{T}\equiv \text{p}$

(b)$\text{p}\wedge F\equiv \text{p}$

Prepare a truth table for the verification of

$\text{p}\wedge \text{T}\equiv \text{p}$

Truth Table

From the truth table, it is true that $\text{p}\wedge F\equiv \text{p}$

(c) localid="1663701873346" $\text{p}\wedge F\equiv F$

Prepare a truth table for the verification of localid="1663701927104" $\text{p}\wedge F\equiv F$

Truth Table

(d) $\text{p}\wedge T\equiv T$

Prepare a truth table for the verification of E

(e) $\text{p}\wedge P\equiv P$

Prepare a truth table for the verification of $\text{p}\wedge P\equiv P$

Truth Table

(e) $\text{p}\wedge p\equiv p$

Prepare a truth table for the verification ofwidth="64">p∧p≡p

From the truth table, it is true that $\text{p}\wedge p\equiv p$

Therefore, all the given logical equivalences have been verified using truth tables.

Truth Table