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Byju's Answer

Standard VI

Mathematics

Idea of a Set

Let A 1, A 2,...

Question

Let $A_{1}, A_{2}, A_{3} . . . . ., A_{40}$ , are 40 sets each with 7 elements and $B_{1}, B_{2}, . . . . . B_{n}$ are n sets each with 7 elements. If $⋃_{i = 1}^{40} A_{i} = ⋃_{j = 1}^{n} B_{j} = S$ and each element of S belongs to exactly ten of A_i's and exactly 9 of B_j's, then n equals

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Solution

The correct option is D
36

n(S) × 10 = 40 × 7

n(S) = 28

28 × 9 = n × 7 ⇒n = 36

Suggest Corrections

Similar questions

Q. Let

A_{1}, A_{2}, A_{3} . . . A_{40}

are 40 sets each with 7 elements and

B_{1}, B_{2}, . . . . . . B_{n}

are n sets each with 7 elements. If

⋃_{i = 1}^{40} A_{i} = ⋃_{j = 1}^{n} B_{j} = S

and each element of S belongs to exactly ten of

A_{i}^{'} s

and exactly 9 of

B_{j}^{'} s

, then n equals

Q. Suppose

A_{1}, A_{2}, . . . . ., A_{30}

are thirty sets each with five elements and

B_{1}, B_{2}, . . . . ., B_{n}

are

n

sets each with three elements such that

⋃_{i = 1}^{30} A_{i} = ⋃_{j = 1}^{n} B_{j} = S

and each element of

S

belongs to exactly

10

of the

A_{i}

's and exactly

9

of the

B_{j}

's. Then

n =

Q. Suppose

A_{1}, A_{2}, . . . ., A_{30}

are thirty sets each having 5 elements and

B_{1}, B_{2}, . . . ., B_{n}

are n sets each with 3 elements. Let

30 ⋃ i = 1 A_{i} = n ⋃ j = 1 B_{j} = S

and each elements of S belongs to exactly 10 of the

A_{i}

and exactly 9 of the

B_{j}

. Then n is equal to-

A_{1}, A_{2}, . . . . . A_{n}

are thirty sets, each with five elements and

B_{1}, B_{2}, . . . . B_{n}

are

n

sets, each with three elements.
Let

⋃_{i = 1}^{30} A_{i} = ⋃_{j = 1}^{n} B_{j} = S

. If each element of

S

belongs to exactly ten of

A_{i}

's and exactly nine of the

B_{j}

's, then

n

Q. Suppose

A_{1}, A_{2}, A_{30}

are thirty sets each with five elements and

B_{1}, B_{2}, ., B_{n}

are in sets each with three elements. Let

30 \cup i = 1 A i = n \cup j = 1 B_{j} = S

. Assume the each element of

S

belongs to exactly ten of the

A_{i}

and exactly

9

B_{j} s

. Find n.

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Let A1,A2,A3. . . . .,A40, are 40 sets each with 7 elements and B1,B2,. . . ..Bn are n sets each with 7 elements. If ⋃40i=1Ai=⋃nj=1Bj=S and each element of S belongs to exactly ten of Ai's and exactly 9 of Bj's, then n equals

The correct option is D 36 n(S) × 10 = 40 × 7 n(S) = 28 28 × 9 = n × 7 ⇒n = 36

Let $A_{1}, A_{2}, A_{3} . . . . ., A_{40}$ , are 40 sets each with 7 elements and $B_{1}, B_{2}, . . . . . B_{n}$ are n sets each with 7 elements. If $⋃_{i = 1}^{40} A_{i} = ⋃_{j = 1}^{n} B_{j} = S$ and each element of S belongs to exactly ten of A_i's and exactly 9 of B_j's, then n equals

The correct option is D
36

n(S) × 10 = 40 × 7

n(S) = 28

28 × 9 = n × 7 ⇒n = 36