How many subsets of the set {1, 2, 3, 4} that contain 3?Select one:a.9b.3c.8d.16
Question
How many subsets of the set {1, 2, 3, 4} that contain 3?
Select one:
- a. 9
- b. 3
- c. 8
- d. 16
Solution
The question is asking for the number of subsets of the set {1, 2, 3, 4} that contain the number 3.
Here are the steps to solve this:
-
First, remove the number 3 from the set, because we know that every subset we're counting must include 3. This leaves us with the set {1, 2, 4}.
-
Now, we need to find the number of subsets of this new set. The number of subsets of a set with n elements is 2^n. In this case, n = 3 (the numbers 1, 2, and 4), so the number of subsets is 2^3 = 8.
-
However, these are the subsets of {1, 2, 4}. Since we know that every subset we're counting must include 3, we can simply add 3 back into each of these subsets. This doesn't change the number of subsets, so the final answer is still 8.
So, the correct answer is c. 8.
Similar Questions
If A={1, 2, 3, 4}, then the number of the subsets of A that contain the element 2 but not 3, is?a.24b.16c.8d.4
Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is :
A set with 4 elements has exactly 16 subsets.Group startsTrue or FalseTrue, unselectedFalse, unselected
Let S={1,2,3,5,7,10,11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____ .
How many functions are there form the set {A, B, C, D} to the set {1, 2, 3}?Select one:a.43b.0c.None of the othersd.34e.12
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.