Answer to Question #264687 in Discrete Mathematics for sarvesh

Question

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)

Answer 1

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)

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