Solution to Let A={a, b, c}, B={d, e}, C={a, d}. Find (i) A × B (ii) B … - Sikademy
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Archangel Macsika

Let A={a, b, c}, B={d, e}, C={a, d}. Find (i) A × B (ii) B × A (iii) A × (B C) (iv) (A C) x B (v) A ∆ (B – C) (vi) Complement of (A ∆ B) (vii) P(B C)

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Here's the Solution to this Question

i)

A × B=\{(a,d),(a,e),(b,d),(b,e),(c,d),(c,e)\}


ii)

B × A=\{(d,a),(d,b),(d,c),(e,a),(e,b),(e,c)\}


iii)

(B C)=\{d\}

A × (B C)=\{(a,d),(b,d),(c,d)\}


iv)

(A C)=\{a\}

(A C) \times B=\{(a,d),(a,e)\}


v)

B – C=\{e\}

A ∆ (B – C)=(A-(B-C))\cup ((B-C)-A)=\{a, b, c\}\cup \{e\}=\{a, b, c,e\}


vi)

A ∆ B=(A-B)\cup (B-A)=\{a, b, c\}\cup \{d, e\}=\{a, b, c,d,e\}

if universal set:

U=\{a, b, c,d,e\}

then complement of (A ∆ B) is empty set \empty


vii)

(B C)=\{d\}

P(B C) is the set of all subsets of (BC)

P(B C)=\{\{\},\{d\}\}

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Question ID: mtid-5-stid-8-sqid-928-qpid-783