Question

truth table of (A+B.C). (A.B)

Answer 1

Answer:

The truth tables for the basic operations are:

And

A B AB

0 0 0

0 1 0

1 0 0

1 1 1

Or

A B A+B

0 0 0

0 1 1

1 0 1

1 1 1

Not

A A

0 1

1 0

For more complicated expressions, tables are built from the truth tables of their basic parts. Here are several:

• Draw a truth table for A+BC.

A B C BC A+BC

0 0 0 0 0

0 0 1 0 0

0 1 0 0 0

0 1 1 1 1

1 0 0 0 1

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

• Draw a truth table for A(B+D).

A B D B+D A(B+D)

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 1 0

1 0 0 0 0

1 0 1 1 1

1 1 0 1 1

1 1 1 1 1

• Draw a truth table for (A+B)(A+C).

A B C A+B A+C (A+B)(A+C)

0 0 0 0 0 0

0 0 1 0 1 0

0 1 0 1 0 0

0 1 1 1 1 1

1 0 0 1 1 1

1 0 1 1 1 1

1 1 0 1 1 1

1 1 1 1 1 1

• Draw a truth table for W(X+Y)Z.

W X Y Z W X+Y W(X+Y) W(X+Y)Z

0 0 0 0 1 0 0 0

0 0 0 1 1 0 0 0

0 0 1 0 1 1 1 0

0 0 1 1 1 1 1 1

0 1 0 0 1 1 1 0

0 1 0 1 1 1 1 1

0 1 1 0 1 1 1 0

0 1 1 1 1 1 1 1

1 0 0 0 0 0 0 0

1 0 0 1 0 0 0 0

1 0 1 0 0 1 0 0

1 0 1 1 0 1 0 0

1 1 0 0 0 1 0 0

1 1 0 1 0 1 0 0

1 1 1 0 0 1 0 0

1 1 1 1 0 1 0 0

• Draw a truth table for PT(P+Z).

P T Z T PT P+Z PT(P+Z)

0 0 0 1 0 0 0

0 0 1 1 0 1 0

0 1 0 0 0 0 0

0 1 1 0 0 1 0

1 0 0 1 1 1 1

1 0 1 1 1 1 1

1 1 0 0 0 1 0

1 1 1 0 0 1 0