Sets and Relations Questions

MathematicsSets and Relations26 Questions Found

MathematicsDomain and Range of a RelationJEE Advanced 1979Moderate

Consider the following relations in the set of real numbers $R$ . $R = {(x, y) : x \in R, y \in R, x^{2} + y^{2} \leq 25}$ $R^{'} = {(x, y) : x \in R, y \in R, y \geq \frac{4}{9} x^{2}}$ Find the domain and range of $R \cap R^{'}$ . Is the relation $R \cap R^{'}$ a function?

Answer:Domain:

{x : x \in R, 16 x^{4} + 81 x^{2} - 2025 \leq 0}

, Range:

{y : y \in R, y \geq \frac{4 x ^{2}}{9}}

MathematicsTypes of Sets and Set OperationsJEE Advanced 1980Easy

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(i) Set $A$ has 3 elements, and set $B$ has 6 elements. What can be the minimum number of elements in the set $A \cup B$ ? (ii) $P, Q, R$ are subsets of a set $A$ . Is the following equality true? $R \times (P^{c} \cup Q^{c})^{c} = (R \times P) \cap (R \times Q)$ ?

Answer:(i) 6 (ii) Yes

MathematicsTypes of Sets and Set OperationsJEE Advanced 1978Easy

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An investigator interviewed 100 students to determine their preferences for the three drinks : milk ( $M$ ), coffee ( $C$ ) and tea ( $T$ ). He reported the following : 10 students had all the three drinks $M, C$ and $T$ ; 20 had $M$ and $C$ ; 30 had $C$ and $T$ ; 25 had $M$ and $T$ ; 12 had $M$ only; 5 had $C$ only; and 8 had $T$ only. Using a Venn diagram find how many did not take any of the three drinks.

Answer:20

MathematicsTypes of Sets and Set OperationsJEE Advanced 1981Easy

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Suppose $A_{1}, A_{2}, \dots, A_{30}$ are thirty sets each with five elements and $B_{1}, B_{2}, \dots, B_{n}$ are $n$ sets each with three elements. Let $⋃_{i = 1}^{30} A_{i} = ⋃_{j = 1}^{n} B_{j} = S$ . Assume that each element of $S$ belongs to exactly ten of the $A_{i}$ 's and to exactly nine of the $B_{j}$ 's. Find $n$ .

Answer:45

MathematicsTypes of Sets and Set OperationsJEE Advanced 1979Easy

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If $X$ and $Y$ are two sets, then $X \cap (X \cup Y)^{c}$ equals.

(A)

X

(B)

Y

(C)

ϕ

(D)

None of these

Answer:C

MathematicsTypes of Sets and Set OperationsJEE Advanced 1998Easy

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In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

(A)

at least 30

(B)

at most 20

(C)

exactly 25

(D)

none of these

Answer:C

MathematicsTypes of RelationsJEE Main 2004Easy

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Let $R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)}$ be a relation on the set $A = {1, 2, 3, 4}$ . The relation R is

(A)

reflexive

(B)

transitive

(C)

not symmetric

(D)

a function

Answer:C

MathematicsTypes of RelationsJEE Main 2005Easy

View in:English Hindi

Let $R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}$ be a relation on the set $A = {3, 6, 9, 12}$ . The relation is

(A)

reflexive and transitive only

(B)

reflexive only

(C)

an equivalence relation

(D)

reflexive and symmetric only

Answer:A

MathematicsTypes of RelationsJEE Main 2006Easy

View in:English Hindi

Let W denote the words in the English dictionary. Define the relation R by $R = {(x, y) \in W \times W ∣ the words x and y have at least one letter in common.}$ Then R is

(A)

not reflexive, symmetric and transitive

(B)

reflexive, symmetric and not transitive

(C)

reflexive, symmetric and transitive

(D)

reflexive, not symmetric and transitive

Answer:B

MathematicsTypes of Sets and Set OperationsJEE Main 2008Easy

View in:English Hindi

The statement $p \to (q \to p)$ is equivalent to

(A)

p \to (p \to q)

(B)

p \to (p \lor q)

(C)

p \to (p \land q)

(D)

p \to (p \leftrightarrow q)

Answer:B

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If X and Y are two sets, then X∩(X∪Y)c equals.

In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let R={(1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A={1,2,3,4}. The relation R is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let R={(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)} be a relation on the set A={3,6,9,12}. The relation is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let W denote the words in the English dictionary. Define the relation R by R={(x,y)∈W×W∣the words x and y have at least one letter in common.} Then R is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The statement p→(q→p) is equivalent to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If X and Y are two sets, then X∩(X∪Y)c equals.

In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let R={(1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A={1,2,3,4}. The relation R is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let R={(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)} be a relation on the set A={3,6,9,12}. The relation is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let W denote the words in the English dictionary. Define the relation R by R={(x,y)∈W×W∣the words x and y have at least one letter in common.} Then R is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The statement p→(q→p) is equivalent to

If $X$ and $Y$ are two sets, then $X \cap (X \cup Y)^{c}$ equals.

Let $R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)}$ be a relation on the set $A = {1, 2, 3, 4}$ . The relation R is

Let $R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}$ be a relation on the set $A = {3, 6, 9, 12}$ . The relation is

Let W denote the words in the English dictionary. Define the relation R by $R = {(x, y) \in W \times W ∣ the words x and y have at least one letter in common.}$ Then R is

The statement $p \to (q \to p)$ is equivalent to

If $X$ and $Y$ are two sets, then $X \cap (X \cup Y)^{c}$ equals.

Let $R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)}$ be a relation on the set $A = {1, 2, 3, 4}$ . The relation R is

Let $R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}$ be a relation on the set $A = {3, 6, 9, 12}$ . The relation is

Let W denote the words in the English dictionary. Define the relation R by $R = {(x, y) \in W \times W ∣ the words x and y have at least one letter in common.}$ Then R is

The statement $p \to (q \to p)$ is equivalent to