True False[1 Marks ]

Question 11 Mark

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then $(\text{A} × \text{B})\cup (\text{A} × \text{C})$
= {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.

Answer

True.
Solution:
Given that: A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6},
A × B = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}
And A × C = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}
$(\text{A} × \text{B})\cup (\text{A} × \text{C})$ = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}

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Question 21 Mark

If $(\text{x}-2, \text{y}+5)=\big(-2, \frac{1}{3}\big)$ are two equal ordered pairs, then $\text{x}=4, \text{y}=\frac{-14}{3}.$

Answer

False.
Solution:
We have, $(\text{x}-2, \text{y}+5)=\big(-2, \frac{1}{3}\big)$
$\Rightarrow\text{x}-2=-2, \text{y}+5=\frac{1}{3}$
$\Rightarrow\text{x}=0, \text{y}=\frac{-14}{3}$

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Question 31 Mark

If A × B = {(a, x), (a, y), (b, x), (b, y)}, then A = {a, b}, B = {x, y}

Answer

True.
Solution:
Given that: A = {a, b} and B = {x, y}
$\therefore$ A × B = {(a, x), (a, y), (b, x), (b, y)}

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Question 41 Mark

If P = {1, 2}, then P × P × P = {(1, 1, 1), (2, 2, 2), (1, 2, 2), (2, 1, 1)}

Answer

False.
Solution:
We have, P = {1, 2} and n(p) = 2
n(P × P × P) = n(P) × n(P) × n(P) = 2 × 2 × 2
= 8 But given P × P × P has 4 elements.

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Question 51 Mark

The ordered pair (5, 2) belongs to the relation $\text{R}=\{(\text{x, y}):\text{y = x}-5, \text{x, y}\in\text{Z}\}$

Answer

False.
Solution:
Given that: $\text{R}=\{(\text{x, y}):\text{y = x}-5, \text{x, y}\in\text{Z}\}$
For (5, 2), y = x - 5
put $\text{x}=5, \text{y}+5-5=0\neq2$
So (5, 2) is not the ordered pair of R.

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