Sets

Question 1

What is the definition of a subset

Answer 1

Let 𝐴 and 𝐵 be sets. We say that 𝐴 is a subset of 𝐵 (or 𝐴 is contained in 𝐵) if every element of 𝐴 is an element of 𝐵, and we denote this by writing 𝐴⊂𝐵.

Question 2

What is the notation of sets

Answer 2

𝐴={𝑥 :”rule for” 𝑥 “to be in” 𝐴}

Question 3

What is the transitive law of subsets

Answer 3

Let 𝐴, 𝐵 and 𝐶 be sets. If 𝐴⊂𝐵 and 𝐵⊂𝐶, then 𝐴⊂𝐶.

Question 4

How can you prove that two sets are equal

Answer 4

Let 𝐴 and 𝐵 be sets. We say that 𝐴 is equal to 𝐵, denoted 𝐴=𝐵 if 𝐴⊂𝐵 and 𝐵⊂𝐴.

Question 5

What is the difference between ( and [ in sets?

Answer 5

( is the same as < (open interval) whereas [ is a closed interval

Question 6

Which set is a subset of every set

Answer 6

The empty set (∅)

Question 7

What are disjoint sets

Answer 7

If 𝐴∩𝐵=∅

Question 8

What is meant by 𝐴∖𝐵

Answer 8

A without B

Question 9

What are the commutative laws of union and intersection

Answer 9

• 𝐴∪𝐵=𝐵∪𝐴
• 𝐴∩𝐵=𝐵∩𝐴

Question 10

What are the associative laws of union and intersection

Answer 10

• (𝐴∪𝐵)∪𝐶=𝐴∪(𝐵∪𝐶)
• (𝐴∩𝐵)∩𝐶=𝐴∩(𝐵∩𝐶)

Question 11

What is the distributive law of intersection over union

Answer 11

𝐴∩(𝐵∪𝐶)=(𝐴∩𝐵)∪(𝐴∩𝐶)

Question 12

What is the distributive law of union over intersection

Answer 12

𝐴∪(𝐵∩𝐶)=(𝐴∪𝐵)∩(𝐴∪𝐶)

Question 13

What are De Morgan’s laws

Answer 13

• (𝐴∪𝐵)′=𝐴′∩𝐵′
• (𝐴∩𝐵)′=𝐴′∪𝐵′

Question 14

What is the cartesian product (AXB)

Answer 14

The set of all ordered pairs (a,b) such that a∈A and b∈B