Let R be the real line- Consider the following sub-sets of the plane R - R S - x - y - y - x -1 and 0- x -2- T - x - y - x - y is an integer- Which of thefollowing is trueA- S is an equivalence relation on R but T is notB- T is an equivalence relation on R but S is notC- Neither S nor T is an equivalence relations on RD- Both S and T are equivalence relations on R

The correct option is B T is an equivalence relation on R but S is not S = (x,y):y = x + 1, 0 lt; x lt; 2 ⇒ S is not symmetric T = (x,y):x y is an inte ...

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Standard XII

Mathematics

Intersection

Let R be the ...

Question

Let R be the real line. Consider the following sub-sets 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 of the following is true

S is an equivalence relation on R but T is not

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T is an equivalence relation on R but S is not

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Neither S nor T is an equivalence relations on R

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Both S and T are equivalence relations on R

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Solution

The correct option is B
T is an equivalence relation on R but S is not

S = {(x,y):y = x + 1, 0 < x < 2}

$\Rightarrow$ S is not symmetric

T = {(x,y):x - y is an integer}

$\Rightarrow$ clearly T is an equivalence

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Similar questions

Q. 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

Q. Let R and S be two equivalence relations on set A. Prove that

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Q. Let

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Statement-l:

A = (x, y) \in R \times R

y - x

is an integer is an equivalence relation on R.
Statement-II:

B = {(x, y) \in R \times R : x = α y

for some rational number

α

} is an equivalence relation on R.

Q. 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?

Q. Let S be a relation on the set R of all real numbers defined by
S = {(a, b) ∈ R × R : a² + b² = 1}
Prove that S is not an equivalence relation on R.

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Let R be the real line. Consider the following sub-sets of the plane R×R S = {x,y}:y = x + 1 and 0 < x < 2, T = {(x,y):x - y} is an integer. Which of the following is true

The correct option is B T is an equivalence relation on R but S is not S = {(x,y):y = x + 1, 0 < x < 2} ⇒ S is not symmetric T = {(x,y):x - y is an integer} ⇒ clearly T is an equivalence

Let R be the real line. Consider the following sub-sets 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 of the following is true

The correct option is B
T is an equivalence relation on R but S is not

S = {(x,y):y = x + 1, 0 < x < 2}

$\Rightarrow$ S is not symmetric

T = {(x,y):x - y is an integer}

$\Rightarrow$ clearly T is an equivalence