Let be the statement ' is divisible by 3' and be the statement ' leaves remainder 1 when divided by 3'. Which of the following is correct? (Here is a positive integer.)
Answer and explanation
Correct answer: B. is both a necessary and a sufficient condition for
- Step 1: Check the three possible remainders of modulo : gives ; gives ; gives .
- Step 2: So is divisible by exactly when : the statements are equivalent.
Answer
is both a necessary and a sufficient condition for .
Why not the others: There are only three cases to check, and exactly one of them makes the expression a multiple of .
Practise more Necessary and sufficient conditions.
Free questions with an explanation for every one, and full timed TMUA mock tests.
More Necessary and sufficient conditions questions
- Let be the statement '' and be the statement ''. Which of the following is correct? (Here is a real number.)
- Let be the statement ' is divisible by 3' and be the statement ' is divisible by 6'. Which of the following is correct? (Here…
- Let be the statement '' and be the statement ''. Which of the following is correct? (Here is a real number.)
- Let be the statement '' and be the statement ' or '. Which of the following is correct? (Here and are…
- Let be the statement '' and be the statement ''. Which of the following is correct? (Here is a real…
- Let be the statement ' is an integer' and be the statement ' is an integer'. Which of the following is correct? (Here is…