Question

How do you use truth tables in logic$?$

Answer 1

Writing truth table:

A truth table represents how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it is constructed. A logic gate truth table shows the possible resultant output depending upon the combination of input(s).

If a two-input logic circuit with input variables $A$and $B$ is used, then there are “four” possible input combinations these are as follows:

1. – “OFF” – “OFF” or $(0,0)$
2. – “OFF” – “ON” or $(0,1)$
3. – “ON” – “OFF” or $(1,0)$
4. – “ON” – “ON” or $(1,1)$

Truth table for $2$-input AND gate:

For AND gate, the output $Q$ is true if both inputs $A$“AND” input $B$are true.

A	B	C
$0$	$0$	$0$
$0$	$1$	$0$
$1$	$0$	$0$
$1$	$1$	$1$

Truth table for $2$-input OR Gate:

For OR gate, the output $Q$ is true if either of input $A$ “OR” input $B$ is true.

A	B	Q
$0$	$0$	$0$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$1$

Truth table for $2$-input NOT gate:

For NOT gate, the output Q is only true when the input is “NOT” true.

A	B
$0$	$1$
$1$	$0$

Hence, We can use truth tables by this manner to determine the truth or falsity of propositional statements by listing all possible outcomes of the truth-values for the included propositions.