Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?
Yes, A ⊂ B because every element of set A is also an element of set B. The elements of A are 'a' and 'b', both of which belong to B. Therefore, A is a subset of B.
A ∪ B = {a, b, c}. The union of two sets consists of all elements from both sets, with common elements taken only once. Since A = {a, b} and B = {a, b, c}, combining all elements gives {a, b, c}.
Explanation
This question tests two fundamental concepts from the chapter: subset and union of sets. For the first part, we apply the definition that A ⊂ B if every element of A is also an element of B. Since 'a' and 'b' from A are both present in B, A is indeed a subset of B. For the second part, we use the definition of union from the textbook: 'The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once.' The union combines all unique elements from both sets.
Solution Steps
Step 1: Check if A ⊂ B by verifying if each element of A belongs to B. Since a ∈ B and b ∈ B, therefore A ⊂ B.
Step 2: Find A ∪ B by listing all elements from both sets A and B, taking common elements only once. A ∪ B = {a, b, c}.