JEE MATHEMATICS MCQ: SET THEORY

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Consider the following statements.

I. If (a, 1), (b, 2) and (c, 1) are in

\mathrm{A} \times \mathrm{B}

and

\mathrm{n}(\mathrm{A})

=3, n(B)=2

, then

A=\{a, b, c\}

and

B=\{1,2\}

II. If

A=\{1,2\}

and

B=\{3,4\}

, then

A \times(B \cap \phi)

is equal to

\mathrm{A} \times \mathrm{B}

.

Choose the correct option.

View answer and explanation

Correct option: A

Only I is true

Option A is correct because statement I is true based on the definition of Cartesian product, while statement II is false since the intersection of any set with the empty set is the empty set.

More Questions from SET THEORY

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Let

S

be the set of all those 2007-place decimal integers

2 a_1 a_2 a_3 \ldots . . a_{2006}

which contain odd number of digit 9 in each sequence

a_1, a_2, a_3, \ldots ., a_{2006}

. The cardinal number of

S

is If

a N=\{a n: n \in N: b N=\{n b: n \in N\}

c N=\{c N: n \in N\}

and

b N \cap c N=d N

, where

a, b, c \in N

and

b, c

are coprime, then Which of the following cannot be the number of elements in the power set of any finite set? If

A=\{x: x

is a multiple of 3

\}

and

B=\{x: x

is a multiple of 5}, then

A-B

is equal to If

F(n)

denotes the set of all divisors of

n

except 1 , what is the least value of y satisfying

[\mathrm{F}(20) \cap \mathrm{F}(16)] \subseteq \mathrm{F}(\mathrm{y})

? In a town of 10000 families, it was found that

40 \%

families buy newspaper

A, 20 \%

families buy newspaper B and

10 \%

families buy newspaper

C

, 5% families buy newspapers

A

and B, 3% buy newspapers B and

C

and

4 \%

buy newspapers

A

and

C

. If

2 \%

families buy all the three newspapers, then number of families which buy

A

only is