Question

Which best describe the meaning of the statement
" if A, then B"?

Answer 1

A mathematical statement generally constitutes of two parts :

• Hypothesis
• Conclusion

In the given statement, "If A, then B" means "A implies B".

Here the conditions that comes under A are the assumptions and the conditions that comes under "B" are the conclusion.

The given Statement "If A, then B" is called logical implication.

The possibilities for the given statement : "If A then B" are :

1. If both A and B are true,

then "A ⇒ B" is also true;

2. If A is true and B is false,

then "A ⇒ B" is false;

3. If A is false but B is true,

then "A ⇒ B" is true;

4. If A and B both are false,

then "A ⇒ B" is true

Answer 2

In general, a mathematical statement consists of two parts: the hypothesis or assumptions, and the conclusion. In your case, "If A, then B" or "A implies B" or "A ⇒ B". The conditions that make up "A" are the assumptions we make, and the conditions that make up "B" are the conclusion. Statement "If A, then B" is called logical implication.

For the "A ⇒ B" there are such possibilities:

1. A and B are both true, then "A ⇒ B" is also true;

2. A true, B false, then "A ⇒ B" is false;

3. A false, B true, then "A ⇒ B" is true;

4. A and B both false, then "A ⇒ B" is true.