Answer:
The three options are;
1) If p = a number is negative and q = the additive inverse is positive, the original statement is p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement the inverse of the original statement is ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q
Step-by-step explanation:
Given a statement if p then q, we have, p → q. The converse of the original statement is then, if q, then p while the inverse of the original statement is then if not p then not q, and the contrapositive statement is then if not q then not p
Mathematically, we have;
The given conditional statement;
If a number is negative, the additive inverse is positive which can be expressed as follows;
The conditional statement is p → q
The converse statement is q → p
The inverse statement is ~p → ~q
The contrapositive statement is ~q → ~p
Therefore, we have;
1) The conditional statement, if p = a number is negative and q = the additive inverse is positive, the original statement which is a conditional statement is therefore p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement, which is a conditional statement is p → q, the inverse of the original conditional statement is therefore, ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the original statement, which is a conditional statement is therefore, q → p, the contrapositive of the original conditional statement is therefore ~p → ~q.
The three options are;
1) If p = a number is negative and q = the additive inverse is positive, the original statement is p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement the inverse of the original statement is ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q
The additive inverse of any number is defined as when it is added to the number it gives zero as a result.
Given a statement if p then q, we have, p → q. The converse of the original statement is then, if q, then p while the inverse of the original statement is then if not p then not q, and the contrapositive statement is then if not q then not p
Mathematically, we have;
The given conditional statement;
If a number is negative, the additive inverse is positive which can be expressed as follows;
The conditional statement is p → q
The converse statement is q → p
The inverse statement is ~p → ~q
The contrapositive statement is ~q → ~p
Therefore, we have;
1) In The conditional statement, if p = a number is negative and q = the additive inverse is positive, the original statement which is a conditional statement is, therefore, p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement, which is a conditional statement is p → q, the inverse of the original conditional statement is, therefore, ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the original statement, which is a conditional statement is, therefore, q → p, the contrapositive of the original conditional statement is, therefore, ~p → ~q
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