Question 1188999: Consider two sets A and B such that A⊆B. Find the possible values of X if A = {2,4,5,x} and B = {2,3,5,6, x+1}.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52812)   (Show Source):
You can put this solution on YOUR website! .
Consider two sets A and B such that A⊆B.
Find the possible values of X if A = {2,4,5,x} and B = {2,3,5,6, x+1}.
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To solve this problem, you should apply some logic.
The logic works this way:
(1) x is NEVER EQUAL to x+1; therefore, x and x+1 represent different elements; they can not represent the same element.
(2) THEREFORE, x of the set A can be and should be one of the explicitly listed elements 2, 3, 5, 6 of the set B.
(3) From the other side, x can not repeat the existing elements 2, 4, 5 of the set A.
(4) It leaves only values 3 or 6 for x.
(5) Now you should check both these possibilities.
If x is 3, then A = {2,4,5,3} and B = {2,3,5,6,4}, which is consistent with the condition A⊆B .
If x is 6, then A = {2,4,5,6} and B = {2,3,5,6,7}, which is NOT CONSISTENT with the condition A⊆B ,
since then the element 4 does belong to A, but does not belong to B.
Thus this check leaves only one UNIQUE possibility for x to be 3.
ANSWER. x is 3.
Solved.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
The solution from the other tutor seems overly complicated....
A = {2,4,5,x} is a subset of B = {2,3,5,6,x+1}
The elements 2 and 5 of set A are also in set B. The element 4 in set A is not explicitly shown in the list of the elements of B; for A to be a subset of B, the element "x+1" in set B must be 4. That makes x equal to 3.
Then, replacing "x" with "3" in set A, and seeing that 3 is an element of set B, we see that the condition is satisfied that A is a subset of B.
ANSWER: x=3
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