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WorksheetsRelations and Functions
Total questions: 10
Worksheet time: 14mins
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
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
f⁻¹og⁻¹
fog
g⁻¹of⁻¹
gof
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
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 (a)
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
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
