U= Whole numbers 1 to 10 A = 2,3,5,7 B = 2,4,6,8,10 C = 1,3,5,7,9 D = 1,4,9 1. A∪B 2. B∪C 3. A∩C 4. C∩D 5. A' 6. B' 7. (A∪C)∩(B∪D) 8. A−B 9. U−A 10. C−D 11. (A−B)∩C (A∪C)' 12. C'∩(A∪D) (A−B)∩C 13. C'∩(A∪D) 14. A∪(B∪C)' 15. (A∪B)∩(C∪D)See answer - CODE PELAJAR

U Whole numbers 1 to 10 A 2357 B 246810 C 13579 D 149 1 AB 2 BC 3 AC 4 CD 5 A 6 B 7 AC BD 8 AB 9 UA 10 CD 11 AB C AC 12 C AD AB C 13 C AD 14 A BC 15 AB CD

Question

U= Whole numbers 1 to 10 A = 2,3,5,7 B = 2,4,6,8,10 C = 1,3,5,7,9 D = 1,4,9 1. A∪B 2. B∪C 3. A∩C 4. C∩D 5. A’ 6. B’ 7. (A∪C)∩(B∪D) 8. A−B 9. U−A 10. C−D 11. (A−B)∩C (A∪C)’ 12. C’∩(A∪D) (A−B)∩C 13. C’∩(A∪D) 14. A∪(B∪C)’ 15. (A∪B)∩(C∪D)

Basic Answer

Step 1: A ∪ B

Union of sets A and B:
A ∪ B = {2, 3, 4, 5, 6, 7, 8, 10}

Step 2: B ∪ C

Union of sets B and C:
B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Step 3: A ∩ C

Intersection of sets A and C:
A ∩ C = {3, 5, 7}

Step 4: C ∩ D

Intersection of sets C and D:
C ∩ D = {1, 9}

Step 5: A’

Complement of set A in U:
A’ = U – A = {1, 4, 6, 8, 9, 10}

Step 6: B’

Complement of set B in U:
B’ = U – B = {1, 3, 5, 7, 9}

Step 7: (A ∪ C) ∩ (B ∪ D)

Union of A and C, then intersection with union of B and D:
A ∪ C = {1, 2, 3, 5, 7, 9}
B ∪ D = {1, 2, 4, 6, 8, 9, 10}
(A ∪ C) ∩ (B ∪ D) = {1, 2, 9}

Step 8: A – B

Difference of sets A and B:
A – B = {3, 5, 7}

Step 9: U – A

Complement of set A in U:
U – A = {1, 4, 6, 8, 9, 10}

Step 10: C – D

Difference of sets C and D:
C – D = {3, 5, 7}

Step 11: (A – B) ∩ C

Difference of A and B, then intersection with C:
A – B = {3, 5, 7}
(A – B) ∩ C = {3, 5, 7}

Step 12: C’ ∩ (A ∪ D)

Complement of C, then intersection with union of A and D:
C’ = {2, 4, 6, 8, 10}
A ∪ D = {1, 2, 3, 4, 5, 7, 9}
C’ ∩ (A ∪ D) = {2, 4}

Step 13: C’ ∩ (A ∪ D)

Complement of C, then intersection with union of A and D:
C’ = {2, 4, 6, 8, 10}
A ∪ D = {1, 2, 3, 4, 5, 7, 9}
C’ ∩ (A ∪ D) = {2, 4}

Step 14: A ∪ (B ∪ C)’

Union of A with complement of union of B and C:
B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(B ∪ C)’ = {}
A ∪ (B ∪ C)’ = {2, 3, 5, 7}

Step 15: (A ∪ B) ∩ (C ∪ D)

Union of A and B, then intersection with union of C and D:
A ∪ B = {2, 3, 4, 5, 6, 7, 8, 10}
C ∪ D = {1, 3, 4, 5, 7, 9}
(A ∪ B) ∩ (C ∪ D) = {3, 4, 5, 7}

Final Answer

1. A ∪ B = {2, 3, 4, 5, 6, 7, 8, 10}
2. B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
3. A ∩ C = {3, 5, 7}
4. C ∩ D = {1, 9}
5. A’ = {1, 4, 6, 8, 9, 10}
6. B’ = {1, 3, 5, 7, 9}
7. (A ∪ C) ∩ (B ∪ D) = {1, 2, 9}
8. A – B = {3, 5, 7}
9. U – A = {1, 4, 6, 8, 9, 10}
10. C – D = {3, 5, 7}
11. (A – B) ∩ C = {3, 5, 7}
12. C’ ∩ (A ∪ D) = {2, 4}
13. C’ ∩ (A ∪ D) = {2, 4}
14. A ∪ (B ∪ C)’ = {2, 3, 5, 7}
15. (A ∪ B) ∩ (C ∪ D) = {3, 4, 5, 7}