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  4. In a Boolean Algebra B , for all x , y in B , x ∧ (x ∨ y) is equal to

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Q. In a Boolean Algebra $ B $ , for all $ x $ , $ y $ in $ B $ , $ x \wedge \left(x \vee y\right) $ is equal to

MHT CETMHT CET 2011

Solution:

$x \wedge(x \vee y)$
$=(x \wedge x) \vee(x \wedge y)$ 'by distribution law'
$=x \vee(x \wedge y)$ 'by idempotent law'
$=(x \vee f)$ 'by contradiction law'
$=x$