Relations and Functions Quiz

If {1, 2, 3} and let R = {(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2)}, Then R is:

• Reflexive, symmetric but not transitive

• symmetric, transitive but not reflexive

• Reflexive and transitive but not symmetric

• an equivalence relation

Let R be a relation defined on Z by aR b if a >= b, Then R is:

• symmetric, transitive but not reflexive

• Reflexive, symmetric but not transitive

• Reflexive and transitive but not symmetric

• an equivalence relation

Let R be a relation defined on Z as follows: (2,2) and (2,5) if a + b = 7, Then domain of R is:

• {3, 4, 5}

• {0, 3, 4, 5}

• {0, 3, 4, 5, ±}

• none of these

The relation R defined on the set {1, 2, 3, 4, 5} by {(a,b) : 16 - a^2 < b} is given by:

• {(1,1), (2,1), (3,1), (4,1), (2,3)}

• {(2,2), (3,2), (4,2), (2,4)}

• {(3,3), (4,3), (5,4), (3,4)}

• none of these

Let R be a relation defined on Z as follows: (x,y) if |x - y| <= 1. Then R is:

• Reflexive and transitive

• Reflexive and symmetric

• Symmetric and transitive

• an equivalence relation

Let {1, 2, 3} and {1, 4, 6, 9} and R is a relation from A to B defined by 'x is greater than y'. Then range of R is given by:

• {1, 4, 6, 9}

• {4, 6, 9}

• {1}

• none of these

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by 'x is relatively prime to y'. Then the domain of R is given by:

• {2, 3, 5}

• {3, 5}

• {2, 3, 4}

• {2, 3, 4, 5}

In the set Z of integers, which of the following relation R is not an equivalence relation?

• if xRy then x <= y

• if xRy then x = y

• if xRy then x - y is an even integer

• if xRy then x mod 3 ≡ y

Let f and g be defined by f(x) = 2x^2 + 3 and g(x) = 4x - 5, then (f o g)(0) is:

• 20

• 25

• 40

• 10

Let f(x) = x and g(x) = x, then (f o g)(1) is given by:

• 0

• 1

• 1

• 2