Consider the statement ? integers m , ? an integer n such that m + n = 0. The fo
ID: 3199600 • Letter: C
Question
Consider the statement
? integers m, ? an integer n such that m + n = 0.
The following are possible ways to express the statement informally without using the symbols ? or ? . Choose ALL answers that match the statement.
A-For any integer you might choose, you can find an integer such that the sum of the two equals 0.
B-Every integer has an additive inverse.
C-An integer has an additive inverse.
D-For every integer you choose, you can find an integer such that the sum of the two not equals 0.
A-For any integer you might choose, you can find an integer such that the sum of the two equals 0.
B-Every integer has an additive inverse.
C-An integer has an additive inverse.
D-For every integer you choose, you can find an integer such that the sum of the two not equals 0.
Explanation / Answer
Solution: The correct options are A), B) and C).
A) For any integer m, we have have the option to choose from all the set of integers. Hence, for all integers m, there exists some integer n such that their sum equals zero.
B) Every integer has an additive inverse means that for all m in Z there exists some n such that m+n=0.
C) An integer m in Z has a additive inverse, thus there exists some n in Z such that m+n =0 is true.
D) The statement is true in general, but does not mean the same as the given statement as it talks of the sum being zero and not non-zero.
Hence, only A), B) and C) are true.