Which of the following equality is not true.

Question

Infinity Learn · Accepted Answer

For equality (a),A ∩ (B$$ ~ $$C) $$=$$ A ∩ (B$$ ∩ C'$$)=$$ ϕ ∪ $$(A$$ ∩ B ∩ C'$$)=$$ $$(A$$ ∩ B∩ A'$$) ∪ (A$$ ∩ B ∩ C'$$)=$$ A ∩ B ∩ $$(A$$' ∪ C'$$)=$$ A∩ B ~ $$(A$$ ∩ $$C)For$$ equality $$(b),A ~ (A$$ ∩ $$B) $$=$$ A ∩ (A$$' ∪ B'$$)=$$ $$(A$$ ∩ A'$$) ∪ (A$$ ∩ B'$$)=$$ ∅ ∪ $$(A$$ ∩ B'$$) $$=$$ A ∩ B' $$=$$ A ~ BFor equality (c)A$$ ~ $$(B$$ ~ $$C) $$=$$ A ~ (B$$ ∩ C'$$) $$=$$ A ∩ (B$$' ∪ $$C)=$$ $$(A$$ ∩ B'$$) ∪ (A$$ ∩ $$C)=$$ $$(A$$ ~ $$B) » (A$$ « $$C)For$$ $$(d) $$LetA={1$$, $$2$$, $$3$$, $$4$$, $$5}$$, $$B={3$$, $$4$$, $$5}$$,$$C={1$$, $$2$$, $$3}So$$, B∆$$C={4$$, $$5}$$ ∪ $${1$$, $$2}={1$$, $$2$$, $$4$$, $$5}Thus$$ A (B$$∆$$C)={3}A$$~ $$B={1$$, $$2}$$; A~ $$C={4$$, $$5}Therefore$$ $$(A$$ ~$$B) ∆ (A$$~ $$C)=({1$$, $$2}$$~ $${4$$, $$5})∪$$({4$$, $$5}$$~ $${1$$, $$2})=$$ $${1$$, $$2}$$ ∪ $${4$$, $$5}$$ $$=$$ $${1$$, $$2$$, $$4$$, $$5)$$.Hence  A ~ (B$$ ∆ $$C) ≠ (A$$ ~ $$B) ∆ (A$$ ~ $$C)

Which of the following equality is not true.

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