Relations and Functions

Maximum number of equivalence relations on the set A = {1,2,3}

Number of relations containing (1,2) and (1,3) in set A = {1,2,3} that are reflexive and symmetric but not transitive.

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

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

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

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

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(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

Number of injective mappings from set A (3 elements) to set B (4 elements)