ISRO2015-10

Question

The boolean expression $\text{AB + A}\text{B}'+\text{A}'\text{C + AC}$ is independent of the boolean variable

• A. $\text{A}$
• B. $\text{B}$
• C. $\text{C}$
• D. None of these

Comments

Detailed Video Explanation: https://youtu.be/DbKnUyyzlZs?t=5498

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I've used kmaps to solve this and there got A+C .so as there's no B in the expression so thought that expression is  independent of B.

Answer 1

$A(B+B')+C(A+A')=A+C$  which is independent on $B$

Option (B) is correct.

Answer 2

Answer is b,

AB+AB'+A'C+AC

A(B+B')+C(A'+A)  ......from property of complementary

A+C ,it is independent of B

Answer 3

We have AB+AB'+A'C+AC

We can rewrite above equation as

AB(C+C')+AB'(C+C')+A'(B+B')C+A(B+B')C ....(As (C+C')=0, (B+B')=0)

We get

ABC+ABC'+AB'C+AB'C'+A'BC+A'B'C+ABC+AB'C

Eliminating Common Terms and rewrite equation as.

ABC+ABC'+AB'C+AB'C'+A'BC+A'B'C

expression in terms of minterms is

m7+m6+m5+m4+m3+m1

K-Map will be

		C'B'	C'B	CB	CB'
		00	01	11	10
A'	0	0	1	1	0
A	1	1	1	1	1

Thus we can write Reduced equation as

A+C

Answer 4

F =  AB + AB′ + A′C + AC

F = A(B + B') + C(A' + A)

F = A.1 + C.1             ( A + A' = 1 )

F = A + C

Here not present B variable

So Option (B) is correct answer

Answer 5

AB + AB' + A'C + AC
= A(B + B') + C(A + A')
= A + C(/pre)
As the expression is independent of 'B', option (B) is correct.