MTH202 Midterm Past Papers by Junaid

Range of function /[f(x)=(e^x)/] is ___________

Composite relation symbolically written as _______

o SoR={(a,c)aeA, ceC, 3eB, (a,b)eR and (b,c)eS} If x=17(mod 5) which of the following integers are valid solution for x ?

o 12

Range of the relation {(0,1),(3,22),(90,34)}

o {1,22,34}

Let A= {0,1,2} and R = {(0,2),(1,1),(2,0)} be a relation on A. The which of the following ordered pairs are needed to make it transitive?

o (0,0) and (2,2)

Operation of subtraction is a binary operation on the set of __________

Let S=R and define the ‘square’ relation R= {(x,y)Ix2=y2}. The square relation is an _________ relation

o Equivalence relation

The logic gate NOT is a uniary operation on {0,1}. o True

Let A= {1,2}, then P(A)=__________

o {{},{1},{2},{1,2}}

If a relation R is reflexive, anti symmetric and transitive then which of the following is not true for the inverse relation. o Inverse relation will be irreflexive. Let R be a binary relation on a set A,R is anti-symmetric iff ___________ o a,beA if (a,b)eR and (b,a)eR then a=b “-“ is a binary operation on the set of integers Z. o True The inverse relation R^(-1) from B to A is defined as ____________ o R^(-1) = {(b,a) e B*A I (a,b)eR}

Which of the following is always true for the matrix representation of a symmetric relation?

o Matrix is equal to its transpose

Let A= {1,2,3,4} and let R and S be transitive binary relations on A defined as; R= {(1,2), (1,3), (2,2), (3,3), (4,2), (4,3) and S={(2,1), (2,4), (3,3)} then RuS= {(1,2), (1,3), (2,1), (2,2), (2,4), (3,3), (4,2), (4,3)}

o R union S is transitive

Let S=R and define the ‘ square’ relation R = {(x,y)Ix2=y2}. The square is an _________ relation.

o Equivalance relation

If x=-10(mod 15). Which of the following integers are valid solution for x?

o 5

o Inverse of R is anti symmetric

If A={1,2,3} is a set and R = {(1,2),(2,2),(2,1)} is a relation on A, R is

Let A={0,1} and B=(1). Let R and S be two binary relations on Cartesian product of A and B such that R={(0,1)} and S= {(1,1)}. Then R intersection S=_________________

o Empty

A relation R is said to be ______ iff it is reflexive, antisymmetric and transitive.

o Partial order Relation

Let X={1,2,3} and Y={7,8,9} and let f be function defined from X to Y such that f is onto then which of the following statement about f is true? o Co-domain of f must contain 1 element

The function fog and gof are always equal

o False

If a relation R={(1,2),(2,3),(3,4)(4,1)(2,2) is given then which of the following is true about this relation.

o R is reflexive

A set is called countable if , and only if, it is____________

o finite

Let f(x) = x2-1 define function f from R to R and c=2 be any scalar, then c,f(x) is __________

o 2x2+2 · The set Z of all integers is ___________ · o Countable