Let A-x-W-thesetofwholenumbersandx-3- B-x-N- thesetofnaturalnumbersand 2-x-4 and C-3-4- then how many elements will A- B- C contain-

Finding the number of elements in (A∪ B)× C:The given set is, A={x∈W,thesetofwholenumbersandx ⇒A ={0,1,2}Also, B={x∈N, the set of natural numbers and 2≤x⇒ B = ...

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Byju's Answer

Standard XII

Mathematics

Properties of Intersection of Sets

Let A=x∈W,the...

Question

Let $A = \{x \in W, the set of whole numbers and x < 3\}, B = \{x \in N, the set of natural numbers and 2 \leq x < 4\}$ and $C = \{3, 4\}$ , then how many elements will $(A \cup B) \times C$ contain?

$6$

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$8$

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$10$

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$12$

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Solution

The correct option is B
$8$

Finding the number of elements in $(A \cup B) \times C$ :
The given set is, $A = \{x \in W, the set of whole numbers and x < 3\}$
$\Rightarrow A = \{0, 1, 2\}$
Also, $B = \{x \in N, the set of natural numbers and 2 \leq x < 4\}$
$\Rightarrow B = \{2, 3\}$
Given, $C = \{3, 4\}$
Therefore, $(A \cup B) = \{0, 1, 2, 3\}$
The number of elements in $A \cup B$ :
$n (A \cup B) = 4$
And, $n (C) = 2$
So, the number of elements in $(A \cup B) \times C$ :
$n [(A \cup B) \times C] = 4 \times 2 = 8$
Hence, the correct answer is option (B).

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Let A=x∈W,thesetofwholenumbersandx<3,B=x∈N,thesetofnaturalnumbersand2≤x<4 and C=3,4, then how many elements will (A∪B)×C contain?

Let $A = \{x \in W, the set of whole numbers and x < 3\}, B = \{x \in N, the set of natural numbers and 2 \leq x < 4\}$ and $C = \{3, 4\}$ , then how many elements will $(A \cup B) \times C$ contain?