(C) Given sets are $A = \{2, 4, 6, 8, 10, \dots\}$,$B = \{5, 10, 15, 20, \dots\}$,and $C = \{10, 20, 30, \dots\}$.Since $C \subset B$,the union $B \cu

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(C) Given sets are $A = \{2, 4, 6, 8, 10, \dots\}$,$B = \{5, 10, 15, 20, \dots\}$,and $C = \{10, 20, 30, \dots\}$.Since $C \subset B$,the union $B \cup C$ is simply $B$.Therefore,$B \cup C = \{5, 10, 15, 20, 25, 30, \dots\} = B$.Now,we find the intersection $A \cap (B \cup C) = A \cap B$.$A \cap B$ represents the set of numbers that are multiples of both $2$ and $5$.The least common multiple of $2$ and $5$ is $10$.Thus,$A \cap B = \{10, 20, 30, \dots\} = C$.

Competitive Quantitative Aptitude Algebra Set Theory

Easy

Let $A = \{x : x \in N \text{ and } x \text{ is a multiple of } 2\}$,$B = \{x : x \in N \text{ and } x \text{ is a multiple of } 5\}$,and $C = \{x : x \in N \text{ and } x \text{ is a multiple of } 10\}$. Describe the set $A \cap (B \cup C)$.

A
$A$
B
$B$
C
$C$
D
None of these

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In a class of $50$ students,$35$ opted for Mathematics and $37$ opted for Biology. How many have opted for both Mathematics and Biology? How many have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects).

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If $A$ and $B$ are two sets,then $A \cap (A \cup B)'$ is equal to

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In a town with a population of $5000$,$3200$ people are egg-eaters,$2500$ are meat-eaters,and $1500$ eat both egg and meat. How many are pure vegetarians?

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If $A = \{x : x \text{ is a multiple of } 3\}$ and $B = \{x : x \text{ is a multiple of } 5\}$,then $A - B$ is ($\bar A$ denotes the complement of $A$).

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Let $A = \{x : x \in N \text{ and } x \text{ is a multiple of } 2\}$,$B = \{x : x \in N \text{ and } x \text{ is a multiple of } 5\}$,and $C = \{x : x \in N \text{ and } x \text{ is a multiple of } 10\}$. Describe the set $A \cap (B \cup C)$.

Similar Questions

In a class of $50$ students,$35$ opted for Mathematics and $37$ opted for Biology. How many have opted for both Mathematics and Biology? How many have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects).

In a certain office,$72 \%$ of the workers prefer cold drink and $44 \%$ prefer tea. If each of them prefers cold drink or tea and $40$ like both,then the total number of workers in the office is

If $A$ and $B$ are two sets,then $A \cap (A \cup B)'$ is equal to

In a town with a population of $5000$,$3200$ people are egg-eaters,$2500$ are meat-eaters,and $1500$ eat both egg and meat. How many are pure vegetarians?

If $A = \{x : x \text{ is a multiple of } 3\}$ and $B = \{x : x \text{ is a multiple of } 5\}$,then $A - B$ is ($\bar A$ denotes the complement of $A$).

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