Use-laws-of-algebra-to-prove-the-following-a-B-A-u-A-B-AuB-AnB-b-A-AnB-A-B-

Question Number 191731 by Spillover last updated on 29/Apr/23

Use laws of algebra to prove the following

(a) [(B - A) u (A - B)] = [(AuB) - (AnB)]

(b) A ▽ (AnB) = A - B

Answered by AST last updated on 29/Apr/23

(a) B - A = B \cap A^{^{'}} a n d A - B = A \cap B^{^{'}}

(B - A) \cup (A - B) = (B \cap A^{'}) \cup (A \cap B^{'})

= {(B \cap A^{^{'}}) \cup A} \cap {(B \cap A^{^{'}}) \cup B^{'}}

= {(A \cup B) \cap (A \cup A^{^{'}})} \cap {(B^{'} \cup B) \cap (B^{^{'}} \cup A^{^{'}})}

= (A \cup B) \cap {(A \cap B)}^{^{'}} = (A \cup B) - (A \cap B)

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