GATE CSE 1998 | Set Theory & Algebra Question 80 | Discrete Mathematics

GATE CSE 1998

MCQ (Single Correct Answer)

-0.6

The binary relation R = {(1, 1)}, (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4) } on the set A = { 1, 2, 3, 4} is

Reflexive, symmetric and transitive

Neither reflexive, nor irreflexive but transitive

Irreflexive, symmetric and transitive

Irreflexive and antisymmetric

GATE CSE 1998

Subjective

-0

Suppose A = {a, b, c, d} and $${\Pi _1}$$ is the following partition of A

$${\Pi _1}\, = \,\{ \{ a,\,\,b,\,\,c\,\} \,,\,\{ d\} \,\} $$
(a) List the ordered pairs of the equivalence relations induced by $${\Pi _1}$$
(b) Draw the graph of the above equivalence relation.

GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

Let R denote the set of real numbers. Let f: $$R\,x\,R \to \,R\,x\,R\,$$ be a bijective function defined by f (x, y ) = (x + y, x - y). The inverse function of f is given by

$${f^{ - 1}}\,(x,\,y)\, = \,\left( {{1 \over {x\, + \,y}},\,{1 \over {x\, - \,y}}} \right)$$

$${f^{ - 1}}\,(x,\,y)\, = \,\,(x\, - \,y,\,\,x\, + y)$$

$${f^{ - 1}}\,(x,\,y)\, = \,\left( {{{x\, + \,y} \over 2},\,{{x\, - \,y} \over 2}} \right)$$

$${f^{ - 1}}\,(x,\,y)\, = \,(2\,(x\, - \,y),\,2\,(x\, + y))$$

GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

Which one of the following is false?

The set of all bijective functions on a finite set forms a group under function composition.

The set {1, 2, ..., p - 1} forms a group under multiplication mod p where p is a prime number.

The set of all strings over a finite alphabet $$\sum $$ forms a group under concatenation.

A subset $$s\, \ne \,\phi $$ of G is a subgroup of the group if and only if for any pair of elements $$a,\,\,b\,\, \in \,\,s,\,\,a\,\,*\,\,{b^{ - 1}}\,\, \in \,s$$.

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