If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A ⊆ B?
Practice Questions
1 question
Q1
If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A ⊆ B?
True
False
Depends on x
None of the above
A is the set of all even integers, while B is the set of multiples of 4. Not all even integers are multiples of 4 (e.g., 2 is even but not a multiple of 4), hence A is not a subset of B.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A ⊆ B?
Solution: A is the set of all even integers, while B is the set of multiples of 4. Not all even integers are multiples of 4 (e.g., 2 is even but not a multiple of 4), hence A is not a subset of B.
Steps: 6
Step 1: Understand what set A is. A is the set of all even integers, which includes numbers like -4, -2, 0, 2, 4, 6, etc.
Step 2: Understand what set B is. B is the set of all multiples of 4, which includes numbers like -8, -4, 0, 4, 8, etc.
Step 3: Determine if every element in set A is also in set B. This means checking if every even integer is a multiple of 4.
Step 4: Find an example of an even integer that is not a multiple of 4. For instance, the number 2 is even but not a multiple of 4.
Step 5: Since we found an even integer (2) that is not in set B, we conclude that not all elements of A are in B.
Step 6: Therefore, we can say that A is not a subset of B, which means A ⊆ B is false.
