Question

using the identities a = a ∩ s and s = b ∪ b and a distributive law to prove that a. a = (a ∩ b) ∪ (a ∩ b)

Answer 1

By using the given identities and the distributive law, we can show that a∙a = (a∩b)∪(a∩b).

Step-by-step explanation:

Using the given identities and the distributive law, we can prove that a∙a = (a∩b)∪(a∩b).

First, let's rewrite the identities in terms of intersection (∩) and union (∪):

a = a∩s

s = b∪b

Next, substitute the values of s and a into the expression:

a∙a = (a∩s)∙(a∩s)

= (a∩(b∪b))∙(a∩(b∪b))

Using the distributive law, we can expand the expression:

= ((a∩b)∪(a∩b))∙((a∩b)∪(a∩b))

= (a∩b)∪(a∩b)