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प्रश्न
Prove the following Boolean expression using the laws and theorems of Boolean algebra.
`("A" + "B") ("A" + overline"B")` = A
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उत्तर
Expand using distributive law
`(A+B)(A+barB) = A(A+barB) + B(A+barB)`
`= (A A+AbarB) + (BA+BbarB)`
`(A+AbarB) + (BA+0)`
`= A+AbarB +AB`
From Absorption Law, A + AB = A
`A+AbarB + AB = A+A(barB+B)`
`barB + B=1`
A + A(1) = A + A = A
Hence proved:
`(A+A(1) = A+A=A`
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संबंधित प्रश्न
Prove the following Boolean expression using the laws and theorems of Boolean algebra.
`"A" (overline"A" + "B")` = AB
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(A + B) (A + C) = A + BC
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