Question

Difficulty: EasySets and Set Operations

If set A={a,b,c,d,e}A = \{a, b, c, d, e\} and set B={c,d,e,f,g}B = \{c, d, e, f, g\}, what is the number of elements in the set (A∖B)∪(B∖A)(A \setminus B) \cup (B \setminus A)?

Answer: 4 / four

Answer

The number of elements in (A∖B)∪(B∖A)(A \setminus B) \cup (B \setminus A) is 4.
The set difference A∖BA \setminus B consists of elements in AA that are not in BB, which gives {a,b}\{a, b\}. Similarly, B∖AB \setminus A consists of elements in BB that are not in AA, giving {f,g}\{f, g\}. The union (A∖B)∪(B∖A)(A \setminus B) \cup (B \setminus A) is {a,b,f,g}\{a, b, f, g\}, which has a cardinality of 4.

Step-by-Step Solution

1
Find the relative difference A∖BA \setminus B
A∖B={a,b}A \setminus B = \{a, b\}
Remove elements of BB present in AA.
2
Find the relative difference B∖AB \setminus A
B∖A={f,g}B \setminus A = \{f, g\}
Remove elements of AA present in BB.
3
Take the union of the two set differences
(A∖B)∪(B∖A)={a,b,f,g}(A \setminus B) \cup (B \setminus A) = \{a, b, f, g\}
Combine elements from both set differences.
4
Count the number of elements in the resulting set
4 elements
The set {a,b,f,g}\{a, b, f, g\} contains 4 distinct elements.

Key Concept

Symmetric Difference of Two Sets
Estimated Time:45s
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