Draw a figure and calculate.
No. of students who passed in one or more subjects = 11 + 9 + 13 + 17 + 15 + 19 + 7 = 91.

Correct Option: A

No. of students who passed in one or more subjects = 11 + 9 + 13 + 17 + 15 + 19 + 7 = 91.
No. of students who failed in all the subjects = 100 – 91 = 9.

As per given question,
(B ∩ C) = {b, c, e} ∩ {b, c, f} = {b, c}
∴ A × (B ∩ C) = {a, d} × {b, c}
= {(a, b), (a, c), (d, b), (d, c)}

Correct Option: B

Given in the question, we can can calculate,
(B ∩ C) = {b, c, e} ∩ {b, c, f} = {b, c}
∴ A × (B ∩ C) = {a, d} × {b, c}
= {(a, b), (a, c), (d, b), (d, c)}
Also, (A × B) ∩ (A × C)
= {(a, b), (a, c), (a, b), (d, c)}
∴ A × (B ∩ C) = (A × B) ∩ (A × C).

We have,
(B ∩ C) = {2, 3, 5, 6, 7} ∩ {5, 6, 7, 8, 9}
= {5, 6, 7}

Correct Option: D

We have,
(B ∩ C) = {2, 3, 5, 6, 7} ∩ {5, 6, 7, 8, 9}
= {5, 6, 7}
∴ A × (B ∩ C) = {a, b} × {5, 6, 7}
= {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7)}.

we can calculate below as per given question,
(B − C) = { b, c, e } – { b, c, f } = { e }
A × (B − C) = { a, d } x { e }
(A × B) = { a, d } x { b, c, e }
(A × C) = { a, d } x { b, c, f }

Correct Option: A

we can calculate below as per given question,
we can calculate below as per given question,
(B − C) = { b, c, e } – { b, c, f } = { e }
A × (B − C) = { a, d } x { e }
(A × B) = { a, d } x { b, c, e }
(A × C) = { a, d } x { b, c, f }
∴ A × (B − C) = {(a, e), (d, e)} ...........…(1)
Also, (A × B) – (A × C) = {(a, e), (d, e)} ..........…(2)
Hence, from (1) and (2), we have
A × (B − C) = (A × B) – (A × C).

A ∩ U = {2, 4, 7} ∩ {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
B ∪ C = {3, 5, 7, 9, 11} ∪ {7, 8, 9, 10, 11}.
Then (A ∩ U) ∩ (B ∪ C) = {2, 4, 7,} ∩ {3, 5, 7, 8, 9, 10, 11}

Correct Option: A

A ∩ U = {2, 4, 7} ∩ {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A ∩ U = {2, 4, 7};
B ∪ C = {3, 5, 7, 9, 11} ∪ {7, 8, 9, 10, 11}.
B ∪ C = {3, 5, 7, 8, 9, 10, 11}.
Then (A ∩ U) ∩ (B ∪ C) = {2, 4, 7,} ∩ {3, 5, 7, 8, 9, 10, 11}
(A ∩ U) ∩ (B ∪ C) = {7}.