A. Deductive Reasoning

In the Warm Up activity you used general statements to draw specific conclusions. This type of thinking is called deductive reasoning. When using deductive reasoning you begin with one or more premises, something you already know to be true. Using these premises, you can draw new conclusions that will also be true.

If your premises are true and your reasoning is correct, deductive reasoning will produce conclusions that you know are true. On the other hand, if a premise is not true or there is a flaw in your reasoning, the conclusion may not be true.

Deductive reasoning can be more valuable than inductive reasoning because the conclusions reached by its use are certain. Unfortunately, deductive reasoning can be more challenging because you need to be certain of your premises, something that can be very difficult.

Example 1

Determine the premises and the conclusion for each of the following.

  1. Medicine Hat is in Alberta and Laya lives in Medicine Hat so Laya lives in Alberta.

    Premises: Medicine Hat is in Alberta; Laya lives in Medicine Hat.

    Conclusion: Laya lives in Alberta.

  2. 350 382 is divisible by 2 because numbers ending with an even digit are divisible by 2.

    Premises: 350 382 ends with an even digit; numbers ending with an even digit are divisible by 2.

    Conclusion: 350 382 is divisible by 2.

  3. If a circle has a radius of 3 cm, then its area is approximately 28 cm2 because .

    Premises: A circle has a radius of 3 cm; .

    Conclusion: The area of the circle is approximately 28 cm2.

Example 2

Decide whether the following conclusions were reached using inductive or deductive reasoning. Explain how you know.

  1. Felix drinks milk because he is a newborn kitten and all newborn kittens drink milk.

    Deductive reasoning is used because a premise that is accepted to be true, "all newborn kittens drink milk", is used to draw a conclusion.

  2. It has rained all week so it will probably rain tomorrow, too.

    Inductive reasoning is used because the conclusion is based on a pattern (recent weather).

  3. The lamp is unplugged and so will not give off light.

    Deductive reasoning is used because a premise that is accepted to be true, although not expressly stated, "a lamp needs electricity to operate", is used to draw a conclusion.

  4. The next letters in the sequence BCD GHI MNO are TUV.

    Inductive reasoning is used because the conclusion is based on a pattern (observed from the letters previously identified in the list).

You need to be careful when using deductive reasoning to ensure that your conclusions follow from the information given. An incorrect use of deductive reasoning can be seen in the following.

An RCMP officer reported that a man driving a blue 2010 Ford truck ran a stop sign. Luke owns a blue 2010 Ford truck. Luke ran the stop sign.

In this case, the conclusion is incorrect because Luke is not the only person who owns a blue 2010 Ford truck.