7. (i) If A=ф and B={-1, 1} then determine the power set of A×B, B×A and B2 (ii ) If A= {0} and B= {1} then determine the A×B and B×A. Also determine P(A×B) and P(B×A) - Advance Math Class 10 - Exercise: 1.2

byAmlesh Mahato •March 24, 2022

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Solution:

(i) Given, A=ф and B={-1, 1}

⇒Now, A×B= ф

B×A= ф

⇒Therefore, P(A×B) ={ ф}

P(B×A)={ ф}

⇒ Again,

$7. (i) If A=ф and B={-1, 1} then determine the power set of A×B, B×A and B2 (ii ) If A= {0} and B= {1} then determine the A×B and B×A. Also determine P(A×B) and P(B×A) - Advance Math Class 10 - Exercise: 1.2$ = B × B

= {-1, 1} × {-1, 1}

= {(-1, -1), (-1, 1), (1, -1), (1, 1)}

⇒ Therefore,

P( B2)= { ф, {(-1, -1)},{ (-1, 1)}, {(1, -1)}, {(1, 1)}, {(-1, -1), (-1, 1)}, {(-1, -1),(1, -1)}, {(-1, -1), (1, 1)}, {(-1, 1), (1, -1)}, {(-1, 1), (1, 1)}, {(1, -1), (1, 1)}, {(-1, -1), (-1, 1), (1, -1)}, {(-1, -1), (-1, 1), (1, 1)}, {(-1, -1), (1, -1), (1, 1)}, {(-1, 1), (1, -1), (1, 1)}, {(-1, -1), (-1, 1), (1, -1), (1, 1)}}

(ii ) Given, A= {0} and B= {1}

⇒ Therefore, A×B = {(0, 1)}

B×A = {(1, 0)}

⇒ P (A×B) = {ф, {(0, 1)}}

⇒ P (B×A) = {ф, {(1, 0)}}

Exercise: 1.2

1. If A = {1, 3, 5} and B= {2, 4, -1} then find A×B and B×A . Find the number of elements in A×B and B×A.

2. (a) If A = {-1, 3, 6} and B= {-3, 5} then find A×B and B×A. Also draw the graph of the Cartesian products.

(b) If A= {2, 4}, B= {-1, 3, 7}, C={1, 0} then with the help of tree diagram find A×B, B×A and A×B×C.

3. If A= {x, y, u, v} and B= {a, b, l, m} then find A×B and represent the Cartesian product by a coordination diagram.

4. If A= {3, 5}, B= {1, 2, 4}, C= {3, 4, 6} then show that

(i) A×(BUC) = (A×B) U (A×C)