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X is the set of all residents in a colon...

X is the set of all residents in a colony and R is a relation defined on X as follows:
''Two persons are related iff they speak the same language''
The relation R, is

A

only symmetric

B

only reflexive

C

both symmetric and reflexive but not transitive

D

equivalence

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-CARTESIAN PRODUCT OF SETS AND RELATIONS -Chapter Test
  1. The relation 'is not equal to' is defined on R, is

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  2. Assertion and Reason type questions :Consider the following statements...

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  3. Let X be the set of all engineering colleges in a state of Indian Repu...

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  4. If R = {(a,b) : a+b=4} is a relation on {1,2,3}, then R is

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  5. If A is a non-empty set, then which of the following is {:(f,a,l,s,e,?...

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  6. If A = {x, y, z}, then the relation R={(x,x),(y,y),(z,z),(z,x),(z,y...

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  7. Assertion and Reason type questions :Consider the following statements...

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  8. The relation ''is a factor of'' on the set N of all natural number is ...

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  9. The relation R={(1,3),(3,5)} is defined on the set with minimum number...

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  10. If a set A contains n elements, then which of the following is the num...

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  11. In a set of teachers of a school, then which of the following cannot b...

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  12. If A={4, 6, 10, 12} and R is a relation defined on A as ''two elements...

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  13. In a set of ants in a locality, two ants are said to be related iff th...

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  14. Let R be a relation defined on S, the set of squares on a chess board ...

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  15. X is the set of all residents in a colony and R is a relation defined ...

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  16. Let A = {ONGC, BHEL, SAIL, GAIL, IOCL} and R be a relation defined as ...

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  17. Let A be the set of all animals. A relation R is defined as ''aRb iff ...

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  18. Consider the non-empty set consisting of children in a family and a r...

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  19. Let A be the set of all student in a school. A relation R is defined o...

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  20. If A and B are two sets such that n(A nn barB)= 9, n( barAnnB)= 10 and...

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