Can anyone show me why
(p + pq) = p.
and
p(p + q) = p.
These proofs are referring to logical operators. Thanks!
(p + pq) = p.
and
p(p + q) = p.
These proofs are referring to logical operators. Thanks!
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There are several ways to show this, but one way is to use the distributive property, i.e brackets can be expanded like this: a(b+c) = ab + bc
(p + pq) = (p1 + pq) = p(1 + q) = p(1) = p
Perhaps a more "intuitive" approach is to reason that pq is a subset of p, so pq adds nothing to p, so p + pq = p
p(p + q) = pp + pq = p1 + pq = p(1 + q) = p(1) + p
(p + pq) = (p1 + pq) = p(1 + q) = p(1) = p
Perhaps a more "intuitive" approach is to reason that pq is a subset of p, so pq adds nothing to p, so p + pq = p
p(p + q) = pp + pq = p1 + pq = p(1 + q) = p(1) + p