SOLUTION: 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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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(52813)   (Show Source): You can put this solution on YOUR website!
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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}.
~~~~~~~~~~~~~~~~~


            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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