Let us start by constructing the truth table for A∨B.
A | B | A∨B |
T | T | T |
T | F | T |
F | T | T |
F | F | F |
Now, let us extend this truth table to include A&(A∨B).
A | B | A∨B | A&(A∨B) |
T | T | T | T |
T | F | T | T |
F | T | T | F |
F | F | F | F |
As we can see that the truth column for A&(A∨B) is the same as the truth table for A. Hence, we can say that A&(A∨B) = A. In other words, the single term which this expression is equal to is A.