# Write a true conditional statement whose inverse is false

### Conditional statement examples

Sufficient condition: p is a sufficient condition for q means "if p then q. Conditional: The conditional of q by p is "If p then q" or "p implies q" and is denoted by p q. A conditional statement is false if hypothesis is true and the conclusion is false. For instance, consider the two following statements: If Sally passes the exam, then she will get the job. A conditional statement is not logically equivalent to its inverse. We will explain this by using an example. Then the law of syllogism tells us that if we turn of the water p then we don't get wet r must be true. Video lesson Write a converse, inverse and contrapositive to the conditional "If you eat a whole pint of ice cream, then you won't be hungry". The part after the "if": you get good grades - is called a hypotheses and the part after the "then" - you will get into a good college - is called a conclusion. Let q stand for the statements "Sally will get the job" and " is divisible by 3". The inverse always has the same truth value as the converse. This means that if p is true then q will also be true. The hypothesis in the first statement is " is divisible by 12", and the conclusion is " is divisible by 3". The converse is "If q then p.

The second statement states that Sally will get the job if a certain condition passing the exam is met; it says nothing about what will happen if the condition is not met. The inverse always has the same truth value as the converse. Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.

If the conditional is true then the contrapositive is true. If we instead use facts, rules and definitions then it's called deductive reasoning. Converse: Suppose a conditional statement of the form "If p then q" is given. The most common patterns of reasoning are detachment and syllogism. Conditional: The conditional of q by p is "If p then q" or "p implies q" and is denoted by p q. Inverse: Suppose a conditional statement of the form "If p then q" is given. A conditional statement is logically equivalent to its contrapositive. If the condition is not met, the truth of the conclusion cannot be determined; the conditional statement is therefore considered to be vacuously true, or true by default.

The example above would be false if it said "if you get good grades then you will not get into a good college".

### Conditional statement logic

If we instead use facts, rules and definitions then it's called deductive reasoning. Let p stand for the statements "Sally passes the exam" and " is divisible by 12". The converse is "If q then p. The hypothesis in the first statement is " is divisible by 12", and the conclusion is " is divisible by 3". Inverse: Suppose a conditional statement of the form "If p then q" is given. It is true if both p and q have the same truth values and is false if p and q have opposite truth values. A conditional statement is not logically equivalent to its converse. The second statement states that Sally will get the job if a certain condition passing the exam is met; it says nothing about what will happen if the condition is not met. Conditional Statements In conditional statements, "If p then q" is denoted symbolically by "p q"; p is called the hypothesis and q is called the conclusion. A conditional statement is not logically equivalent to its inverse. Let q stand for the statements "Sally will get the job" and " is divisible by 3". Sufficient condition: p is a sufficient condition for q means "if p then q. If the conditional is true then the contrapositive is true. For instance, consider the two following statements: If Sally passes the exam, then she will get the job.
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