Mathematics
Grade9
Easy
Question
Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily; therefore,
- Look out for the snowplows while driving to school.
- The big test will not be given today.
- The roads will be hard to drive on.
- You should call the school to see if the school is canceled.
Hint:
Reasoning is drawing conclusions using statements and pictures. There are two types of reasonings they are deductive and inductive. In deductive reasoning we use facts or general statements to draw a general conclusion. There are two laws under deductive reasoning they are Law of Detachment and Law of Syllogism. Here, we have to draw a conclusion using the given statements.
The correct answer is: The big test will not be given today.
In the question the given statements are
1. If it is snowing heavily, then school will be canceled.
2. If school is canceled, the big test will not be given today.
Here, we have to complete the concluding statement It is snowing heavily; therefore, using the law of syllogism.
Let statement (1) be p, statement (2) be q and the conclusion be r.
In syllogism if p equals q and q equals r then p equals r.
So, the conclusion will be If it is snowing heavily, then the big test will not be given today.
Thus, the complete concluding statement will be If it is snowing heavily, then the big test will not be given today.
Therefore, the correct option is b, i.e., the big test will not be given today.
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.
