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7 Maths Exercise Solutions

- R is reflexive and transitive but not symmetric.
- R is an equivalence relation.
- R is reflexive and symmetric but not transitive.
- R is symmetric and transitive but not reflexive.
- (3, 8) R
- (2, 4) R
- (6, 8) R
- (8, 7) R

Determine whether the below relation is reflexive, symmetric and transitive:

Relationon the set of natural numbers is defined as

Relationon the set of natural numbers is defined as

Determine whether the relation is reflexive, symmetric and transitive:

Relation R in the set A of human beings in a town at a particular time given by

R = {(x, y) : x is exactly 7 cm taller than y}

Relation R in the set A of human beings in a town at a particular time given by

R = {(x, y) : x is exactly 7 cm taller than y}

Show the relation in the set , given by

is a multiple of is an equivalence relation.

Find the set of all elements related to 1 in each case.

is a multiple of is an equivalence relation.

Find the set of all elements related to 1 in each case.

Show that the relation on the set , given by

, is an equivalence relation. Find the set of all elements related to .

, is an equivalence relation. Find the set of all elements related to .

Show that the relation R defined in the set A of all triangles as R = {(T_{1}, T_{2}) : T_{1} is similar to T_{2}}, is an equivalence relation. Consider three right angle triangles T_{1} with sides 3, 4, 5, T_{2} with sides 5, 12, 13 and T_{3} with sides 6, 8, 10. Which triangles among T_{1}, T_{2} and T_{3} are related?

Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.

Let R be the relation on the set N given by R = {(a, b) : a = b – 2, b > 6}. Which of the the following is true:

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