A' + AB' = A'+B'

Question

Can somebody please prove A'+ AB' = A' + B'  using both methods vann diagram and alegebric simplification.

Please upload the pic of Vann Daigram.Thanks!

Answer 1

A' + AB' = A'B + A'B' + AB'
= A'B + A'B' +A'B' + AB'
= A'(B+B') + B'(A'+A)
= A' + B'

Alternatively (much better approach)

A' + AB' will become TRUE if A' is true or if AB' is true. If A' is true we don't need to consider AB' and if A' is false, it means A is true and hence we need to consider only B'.

Comments

I think the last approach is for the shorter expressions ..with larger expressions it wl get complex ryt?

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Later I got another idea to solve it A' + AB',apply distributive property, that comes to
(A'+A)(A'+B') = A'+B'

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Yes. That approach is specific to this question. But while solving large equations, this form usually comes and there you can use this logic to quickly proceed further.

Answer 2

A'+AB'

(A'+A) (A'+B')  BY DISTRIBUTED LAW

A'+A =1 BY IDENTITY LAW

1.(A'+B')

A'+B'