Sets and Relations Questions

MathematicsSets and Relations26 Questions Found

MathematicsTypes of Sets and Set OperationsJEE Main 2008Easy

View in:English Hindi

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number". Statement-1 : r is equivalent to either q or p Statement-2 : r is equivalent to ~(p <-> q).

MathematicsTypes of RelationsJEE Main 2008Easy

View in:English Hindi

Let $R$ be the real line. Consider the following subsets of the plane $R \times R$ : $S = {(x, y) : y = x + 1 and 0 < x < 2}$ , $T = {(x, y) : x - y is an integer}$ . Which one of the following is true?

(A)

Neither S nor T is an equivalence relation on R

(B)

Both S and T are equivalence relation on R

(C)

S is an equivalence relation on R but T is not

(D)

T is an equivalence relation on R but S is not

Answer:D

MathematicsTypes of Sets and Set OperationsJEE Main 2009Easy

View in:English Hindi

If A, B and C are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then

(A)

A=C

(B)

B=C

(C)

A \cap B = \phi

(D)

A=B

Answer:B

MathematicsTypes of Sets and Set OperationsJEE Main 2009Easy

View in:English Hindi

Statement-1: $\sim (p \leftrightarrow\sim q)$ is equivalent to $p \leftrightarrow q$ . Statement-2: $\sim (p \leftrightarrow\sim q)$ is a tautology

(A)

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(B)

Statement-1 is true, Statement-2 is false.

(C)

Statement-1 is false, Statement-2 is true.

(D)

Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement -1

Answer:B

MathematicsTypes of RelationsJEE Main 2010Easy

View in:English Hindi

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S = {( $\frac{m}{n}, \frac{p}{q}$ ) | m, n, p and q are integers such that $n, q \neq = 0$ and qm = pn}. Then

(A)

Neither R nor S is an equivalence relation

(B)

S is an equivalence relation but R is not an equivalence relation

(C)

R and S both are equivalence relations

(D)

R is an equivalence relation but S is not an equivalence relation

Answer:B

MathematicsRepresentation of SetsJEE Main 2010Easy

View in:English Hindi

Let S be a non-empty subset of R. Consider the following statement : P : There is a rational number $x \in S$ such that $x > 0$ . Which of the following statements is the negation of the statement P ?

(A)

There is no rational number

x \in S

such than

x \leq 0

(B)

Every rational number

x \in S

satisfies

x \leq 0

(C)

x \in S

and

x \leq 0 \Rightarrow x

is not rational.

(D)

There is a rational number

x \in S

such that

x \leq 0

Answer:B

MathematicsRepresentation of SetsJEE Main 2011Easy

View in:English Hindi

Consider the following statements P: Suman is brilliant Q: Suman is rich R : Suman is honest The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

(A)

\sim (Q \leftrightarrow (P \land \sim R))

(B)

\sim Q \leftrightarrow\sim P \land R

(C)

\sim (P \land \sim R) \leftrightarrow Q

(D)

\sim P \land (Q \leftrightarrow\sim R)

Answer:A

MathematicsTypes of RelationsJEE Main 2011Easy

View in:English Hindi

Let R be the set of real numbers. Statement-1: $A = {(x, y) \in R \times R : y - x is an integer}$ is an equivalence relation on R. Statement-2: $B = {(x, y) \in R \times R : x = α y for some rational number α}$ is an equivalence relation on R.

(A)

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(B)

Statement-1 is true, Statement-2 is false.

(C)

Statement-1 is false, Statement-2 is true.

(D)

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Answer:B

MathematicsTypes of Sets and Set OperationsJEE Main 2012Easy

View in:English Hindi

The negation of the statement "If I become a teacher, then I will open a school", is :

(A)

I will become a teacher and I will not open a school.

(B)

Either I will not become a teacher or I will not open a school.

(C)

Neither I will become a teacher nor I will open a school.

(D)

I will not become a teacher or I will open a school.

Answer:A

MathematicsTypes of Sets and Set OperationsJEE Main 2013Easy

View in:English Hindi

Consider Statement-1 : $(p \land \sim q) \land (\sim p \land q)$ is a fallacy. Statement-2 : $(p \to q) \leftrightarrow (\sim q \to\sim p)$ is a tautology.

(A)

Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

(B)

Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-I.

(C)

Statement-1 is true; Statement-2 is false.

(D)

Statement-1 is false; Statement-2 is true.

Answer:B

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number". Statement-1 : r is equivalent to either q or p Statement-2 : r is equivalent to ~(p <-> q).

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let R be the real line. Consider the following subsets of the plane R×R: S={(x,y):y=x+1 and 0<x<2}, T={(x,y):x−y is an integer}. Which one of the following is true?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If A, B and C are three sets such that A∩B=A∩C and A∪B=A∪C, then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Statement-1: ∼(p↔∼q) is equivalent to p↔q. Statement-2: ∼(p↔∼q) is a tautology

Consider the following statements P: Suman is brilliant Q: Suman is rich R : Suman is honest The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

The negation of the statement "If I become a teacher, then I will open a school", is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider Statement-1 : (p∧∼q)∧(∼p∧q) is a fallacy. Statement-2 : (p→q)↔(∼q→∼p) is a tautology.

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number". Statement-1 : r is equivalent to either q or p Statement-2 : r is equivalent to ~(p <-> q).

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let R be the real line. Consider the following subsets of the plane R×R: S={(x,y):y=x+1 and 0<x<2}, T={(x,y):x−y is an integer}. Which one of the following is true?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If A, B and C are three sets such that A∩B=A∩C and A∪B=A∪C, then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Statement-1: ∼(p↔∼q) is equivalent to p↔q. Statement-2: ∼(p↔∼q) is a tautology

Consider the following statements P: Suman is brilliant Q: Suman is rich R : Suman is honest The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

The negation of the statement "If I become a teacher, then I will open a school", is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider Statement-1 : (p∧∼q)∧(∼p∧q) is a fallacy. Statement-2 : (p→q)↔(∼q→∼p) is a tautology.

Let $R$ be the real line. Consider the following subsets of the plane $R \times R$ : $S = {(x, y) : y = x + 1 and 0 < x < 2}$ , $T = {(x, y) : x - y is an integer}$ . Which one of the following is true?

If A, B and C are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then

Statement-1: $\sim (p \leftrightarrow\sim q)$ is equivalent to $p \leftrightarrow q$ . Statement-2: $\sim (p \leftrightarrow\sim q)$ is a tautology

Consider Statement-1 : $(p \land \sim q) \land (\sim p \land q)$ is a fallacy. Statement-2 : $(p \to q) \leftrightarrow (\sim q \to\sim p)$ is a tautology.

Let $R$ be the real line. Consider the following subsets of the plane $R \times R$ : $S = {(x, y) : y = x + 1 and 0 < x < 2}$ , $T = {(x, y) : x - y is an integer}$ . Which one of the following is true?

If A, B and C are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then

Statement-1: $\sim (p \leftrightarrow\sim q)$ is equivalent to $p \leftrightarrow q$ . Statement-2: $\sim (p \leftrightarrow\sim q)$ is a tautology

Consider Statement-1 : $(p \land \sim q) \land (\sim p \land q)$ is a fallacy. Statement-2 : $(p \to q) \leftrightarrow (\sim q \to\sim p)$ is a tautology.