Question

If A={5,6} , B={4,5,6},C={5,6,7}, show that A×A=(B×B)n(C×C).

Answer 1

(5×6)=(4×5×6)n(5×6×7)

Answer 2

Answer:

Given: A={5, 6}, B={4, 5,6}, C={5, 6,7}.

A×A={5, 6}×{5, 6}.

A×A={(5, 5), (5, 6),(6, 5), (6, 6).-->1

B×B={4, 5,6}×{4, 5,6}.

B×B={(4, 4), (4, 5), (4, 6), (5, 4), (5, 5),

(5, 6) ,(6, 4), (6, 5), (6, 6).

C×C={5, 6,7}×{5, 6,7}.

C×C={(5, 5), (5, 6), (5, 7), (6, 5), (6, 6),

(6, 7), (7, 5),(7, 6), (7, 7).

(B×B)∩(C×C) ={(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6,6) }∩{(5, 5), (5, 6), (5, 7), (6, 5), (6, 6), (6, 7), (7, 5),

(7, 6) , (7, 7)}.

(B×B) ∩(C×C) ={(5, 5), (5, 6), (6, 5),

(6, 6) } -->2

From Equation 1 and 2 we get.

A×A=(B×B)∩(C×C)

Step-by-step explanation:

@Dare