Consider the statement, \" If A is a subset of B, then A U B = B.\" The lines be
ID: 3119906 • Letter: C
Question
Consider the statement, " If A is a subset of B, then A U B = B."
The lines below form a supposed proof of this statement. Select the first line that is either incorrect or does not follow from the lines above it. If the proof is correct, select the last option.
Options:
Let A be a subset of B. By definition of union, B is a subest of A U B.
Now let x be an element of A U B. Then x is in A or x is in B.
If x is in A, then x is also in B since A is a subest of B. Hence, if x is in A U B, then x is in B and A UB is a subset of B.
Since B is a subset of A U B and A U B is a subset of B, we have, by definition that A U B = B.
Let A be a subset of B. By definition of union, B is a subest of A U B.
Now let x be an element of A U B. Then x is in A or x is in B.
If x is in A, then x is also in B since A is a subest of B. Hence, if x is in A U B, then x is in B and A UB is a subset of B.
Since B is a subset of A U B and A U B is a subset of B, we have, by definition that A U B = B.
Explanation / Answer
All lines are correct
a) yes by definition B is a subset of A U B
since AUB containes B
b) if x is in A U B , x is in A or in B or in both
c) if x is in A and A is a subset of B so x is in B hence if x is in AUB then x is in B
d) right