Relations and Functions

The maximum number of equi

valence relations on the set A = {1,2,3} are

• 1

• 2

• 3

• 5

Let A = {1,2,3}. Then the number of relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is

• 1

• 2

• 3

• 4

Let f:ℝ-->ℝ be defined by f(x)= 1/x, for all x∈ℝ.Then f is

• one one

• onto

• bijective

• f is not defined

Tags

CCSS.HSF-BF.B.4D

Which of the following functions from ℤ to ℤ are bijections?

• f(x)=x³

• f(x)=x+2

• f(x)=2x+1

• f(x)=x²+1

Tags

CCSS.HSF-BF.B.4D

Let f:A-->B and g:B-->C are bijective functions. Then (gof)⁻¹ is

• f⁻¹og⁻¹

• fog

• g⁻¹of⁻¹

• gof

Tags

CCSS.HSF-BF.B.4A

Let * be binary operation defined on ℝ by a*b=1+ab, for all a,b∈ℝ. Then the operation * is

• commutative but not associative

• associative but not commutative

• neither commutative nor associative

• both commutative and associative

Tags

CCSS.6.EE.A.3

Let ℝ be the set of real numbers and * be the binary operation defined on ℝ as a*b =a +b -ab for all a,b ∈ℝ. Then the identity element with respect to the binary operation * is__________

For real numbers x and y define xRy if and only if x-y+sqrt root(2) is an irrational number. Then the relation R is

• Reflexive

• Symmetric

• Transitive

• none of the above

Let f:ℝ-->ℝ be defined by f(x) = sinx and g:ℝ-->ℝ be defined by g(x) = x ², the fog is

• x²sinx

• (sinx)²

• sinx²

• sinx/x²

Tags

CCSS.HSF-BF.A.1C

Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is

• 144

• 12

• 24

• 64