1.7 Observation and Logical Thinking

Using deductive reasoning, 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, then...

• 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 school is canceled.

What conclusion can be drawn from the following statements?
If the stereo is on, then the volume is loud.  
If the volume of the stereo is loud, then the neighbors will complain.

• If the neighbors complain, then the stereo will be loud.
• If the stereo is on, then the neighbors will complain.
• If the stereo is volume is loud, then the stereo is on.
• If the stereo is on, then the volume is loud.

What conclusion can be drawn from the following statements?
If the sun is shining, then it is a beautiful day.  
If it is a beautiful day, then we will have a picnic.

• If the sun is shining, then it is a beautiful day.
• If it is a beautiful day, then the sun is shining.
• If the sun is shining, then we will go on a picnic.
• If we go on a picnic, then the sun is shining.

Which of the following statements is valid based on the given scenario?
If Jason plays basketball, then Steve sits on the bench.  
If Steve sits on the bench, then Ronald starts at center.  

• If Steve sits on the bench then Jason plays basketball.
• If Ronald starts at center then Jason plays basketball.
• If Steve sits the bench then Ronald does not start at center.
• If Jason plays basketball then Ronald starts at center.

Determine if inductive or deductive reasoning is being used.

Blake knows that if there is a snow storm, then the roads will be slick.

The roads are slick.

Therefore, Blake concludes there was a snow storm.

• Inductive

• Deductive

What is a conjecture?

• A statement that has been proven true.

• An unproven statement based on observations.

• A statement that has been proven false.

• An unproven statement that is assumed false.

What can you conclude from this information?

"If you study, then you will pass the test. If you pass the test, then you will pass the course."

• You did not study.

• You did not pass the course.

• If you study, then you will pass the course.

• You passed the test.

The Giants have lost their last seven games. Thus, they will probably lose their next game.

What type of reasoning was used?

• Inductive

• Deductive

All students go to school. You are a student. Therefore you go to school.

What type of reasoning was used?

• Inductive

• Deductive

You see the numbers 2, 4, .... and decide the next number must be a 6

What type of reasoning was used?

• Inductive

• Deductive