English for Maths I



English for Maths I

Week 2 Deductive reasoning

TASK 1. Watch the ppt on inductive vs deductive and work with a partner to decide what can go wrong.

TASK 2. Read the text on deductive reasoning and complete the missing information: Specific examples reasoning premises

Deductive reasoning, also deductive logic or logical deduction or, informally, "top-down" logic, is the process of ………………………reasoning from one or more general statements (premises) to reach a logically certain conclusion.

Deductive reasoning links ………………………premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true.

Deductive reasoning (top-down logic) contrasts with inductive reasoning (bottom-up logic) in the following way: In deductive reasoning, a conclusion is reached from general statements, but in inductive reasoning the conclusion is reached from ………………………specific examples. (Note, however, that the inductive reasoning mentioned here is not the same as induction used in mathematical proofs - mathematical induction is actually a form of deductive reasoning.)

From Wikipedia, the free encyclopedia

Task 3. Read the following text on Law of detachment, Syllogism and contrapositive and match the examples with the respective laws. Then give an example of your own to justify what is stated.

A Simple Example

An example of a deductive argument:

1. All men are mortal.

2. Aristotle is a man.

3. Therefore, Aristotle is mortal.

The first premise states that all objects classified as "men" have the attribute "mortal". The second premise states that "Aristotle" is classified as a "man" – a member of the set "men". The conclusion then states that "Aristotle" must be "mortal" because he inherits this attribute from his classification as a "man".

Law of Detachment

The law of detachment (also known as affirming the antecedent and Modus ponens) is the first form of deductive reasoning. A single conditional statement is made, and a hypothesis (P) is stated. The conclusion (Q) is then deduced from the statement and the hypothesis. The most basic form is listed below:

1. P→Q (conditional statement)

2. P (hypothesis stated)

3. Q (conclusion deduced)

In deductive reasoning, we can conclude Q from P by using the law of detachment. However, if the conclusion (Q) is given instead of the hypothesis (P) then there is no valid conclusion. EXAMPLE missing.

Law of Syllogism

The law of syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form, with the true premise P:

1. P→Q

2. Q→R

3. Therefore, P→R.

Example missing. We deduce the final statement by combining the hypothesis of the first statement with the conclusion of the second statement. We also allow that this could be a false statement. This is an example of the Transitive Property in mathematics. The Transitive Property is many times phrased in this form:

1. A=B

2. B=C

3. Therefore A=C

Law of Contrapositive

The law of contrapositive states that, in a conditional, if the conclusion is false, then the hypothesis must be false also. The general form is the following:

1. P→Q

2. ~Q

3. Therefore we can conclude ~P.

Example missing.

Example A: The following is an example of an argument in the form of an if-then statement:

1. If an angle satisfies 90° ................
................

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