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Q: What is the converse inverse and contrapositive If every digit of a number is divisible by 3 then the number is divisible by 3?

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If a number is not divisible by 3 then it is not divisible by 9.

If a number is not divisible by two then it is not an even number.

If this is a T-F question, the answer is false. It is true that if a number is divisible by 6, it also divisible by 3. This is true because 6 is divisible by 3. However, the converse -- If a number is divisible by 3, it is divisible by 6, is false. A counterexample is 15. 15 is divisible by 3, but not by 6. It becomes clearer if you split the question into its two parts. A number is divisible by 6 if it is divisible by 3? False. It must also be divisible by 2. A number is divisible by 6 only if it is divisible by 3? True.

"contrapositive" refers to negating the terms of a statement and reversing the direction of inference. It is used in proofs. An example makes it easier to understand: "if A is an integer, then it is a rational number". The contrapositive would be "if A is not a rational number, then it cannot be an integer". The general form, then, given "if A, then B", is "if not B, then not A". Proving the contrapositive generally proves the original statement as well.

The additive inverse of a number is that which when added to the number gives 0. If n is a number then the additive inverse of it (-n) is that number such that: n + -n = 0 For example, the additive inverse of '4' is '-4'.

Related questions

Look at the statement If 9 is an odd number, then 9 is divisible by 2. The first part is true and second part is false so logically the statement is false. The contrapositive is: If 9 is not divisible by 2, then 9 is not an odd number. The first part is true, the second part is false so the statement is true. Now the converse of the contrapositive If 9 is not an odd number, then 9 is not divisible by two. The first part is false and the second part is true so it is false. The original statement is if p then q,the contrapositive is if not q then not p and the converse of that is if not p then not q

Converse: If a number ends in 0,2,4,6, or 8 then it is even. Inverse: If a number does not end in 0,2,4,6, or 8 then it is not even. Contrapositive: If a number is not even, then it does not end in 0,2,4,6, or 8.

If a number is not divisible by 3 then it is not divisible by 9.

If a number is not divisible by two then it is not an even number.

If a number is not even, then it is not divisible by 2.

If this is a T-F question, the answer is false. It is true that if a number is divisible by 6, it also divisible by 3. This is true because 6 is divisible by 3. However, the converse -- If a number is divisible by 3, it is divisible by 6, is false. A counterexample is 15. 15 is divisible by 3, but not by 6. It becomes clearer if you split the question into its two parts. A number is divisible by 6 if it is divisible by 3? False. It must also be divisible by 2. A number is divisible by 6 only if it is divisible by 3? True.

A simple example of a conditional statement is: If a function is differentiable, then it is continuous. An example of a converse is: Original Statement: If a number is even, then it is divisible by 2. Converse Statement: If a number is divisible by 2, then it is even. Keep in mind though, that the converse of a statement is not always true! For example: Original Statement: A triangle is a polygon. Converse Statement: A polygon is a triangle. (Clearly this last statement is not true, for example a square is a polygon, but it is certainly not a triangle!)

"contrapositive" refers to negating the terms of a statement and reversing the direction of inference. It is used in proofs. An example makes it easier to understand: "if A is an integer, then it is a rational number". The contrapositive would be "if A is not a rational number, then it cannot be an integer". The general form, then, given "if A, then B", is "if not B, then not A". Proving the contrapositive generally proves the original statement as well.

An inverse number is an opposing number of the standard number. For example, if a standard number is 12 then the inverse is -12.

How can the following definition be written correctly as a biconditional statement? An odd integer is an integer that is not divisible by two. (A+ answer) An integer is odd if and only if it is not divisible by two

The phone number of the Converse Branch is: 318-567-3121.

No. If the number of the year is not divisible by 4 (and 1998 is not) it cannot be a leap year. Incidentally, the converse is not strictly true - a year that is divisible by four is nearly but not always a leap year.

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