Mathematics

Grade9

Easy

Question

# If statements 1 and 2 are true, is statement 3 a valid conclusion by the law of syllogism? Why or why not?

Statement 1: If you are studying the Gettysburg Address, then you are studying the Civil War.

Statement 2: If you are studying the Civil War, then you are a History Major.

Statement 3: If you are studying the Gettysburg Address, then you are a history major.

- Valid
It follows the pattern for the law of syllogism.
If p, then q.
If q, then r.
If p, then r
- Invalid
It does not follow the pattern for the law of syllogism.
If p, then q.
If p, then r.
If q, then r.
- Valid
It follows the pattern for the law of syllogism.
If q, then p.
If p, then q.
If p, then r.
- Invalid
It does not follow the pattern for the law of syllogism.
If q, then r.
If p, then r.
If p, then q.

Hint:

### In deductive reasoning we use facts, definitions and postulates to draw a conclusion. There are two laws under deductive reasoning they are Law of Detachment and Law of Syllogism. Here, we have to determine which of these laws in applied here to draw the conclusion.

## The correct answer is: Valid

It follows the pattern for the law of syllogism.

If p, then q.

If q, then r.

If p, then r

### In the question it is given that,

Statement 1: If you are studying the Gettysburg Address, then you are studying the Civil War.

Statement 2: If you are studying the Civil War, then you are a History Major.

Statement 3: If you are studying the Gettysburg Address, then you are a history major.

Here, we have to determine the whether Law of Syllogism is applied here or not.

Let statement (1) be p, statement (2) be q and statement (3) be r.

From the given statement we can say that p equals to q and q equals r.

So, p equals r.

Thus, the above statements are valid.

Therefore, the correct option is valid.

In Law of Syllogism if a statement p equals q and if q equals r, then p equals r whereas in Law of Detachment if a statement p equals q where p is true then q is also true.