Disjunctive Syllogism

The disjunctive syllogism is a syllogism whose major premise is a disjunctive proposition

The disjunctive proposition is one, which presents two or more alternatives, one of which is true. Its members are linked by the conjunctions “either…or”

STRICT DISJUNCTIVE

The strict disjunctive proposition is one in which only one member (called alternant) is true and others are false.

Example:

Either you are single or married

Rules for Strict Disjunctive Syllogism

1. Affirm one or more alternants in the minor premise and deny the other alternants in the conclusion.

The President is either a Democrat, Republican or LiberalThe President is Democrat.Therefore, the President is neither a Republican nor liberal

Rule No. 2

Deny one or more alternants in the minor premise and affirm the remaining alternants in the conclusion.

The chair I am sitting is either made of wood or steelIt is not made of wood.Therefore, it is made of steel.

BROAD DISJUNCTIVE

The broad disjunctive proposition is one in which one or more alternants may be true.

“He got a failing mark because he is either lazy or dull.”

Rule for Broad Disjunctive Syllogism

Deny one or more alternants in the minor premise and affirm the remaining alternants in the conclusion.

Ate Joy sews either skirts or blousesBut she does not sew blousesTherefore, She sews skirts

EXERCISES IN DISJUNCTIVE SYLLOGISM

1. Julius is either tall or short.But Julius is not tall.Therefore, he is short.

2. Gary V. is either a singer or an actorBut Gary V. is a singer.Therefore, he is not an actor

3. It is either, winter, autumn, summer or spring. But it is neither winter nor autumn Therefore, it is either summer or spring

4. He was overspeeding or the cop’s speedometer was defective. But he was not overspeeding. Therefore, the cop’s speedometer was defective.

5. Darwin and Ate Fe or both should attend the meeting. Darwin will attend the meeting. Therefore, Ate Fe will not attend it.

CONJUNCTIVE SYLLOGISM – the major premise is acompound proposition

The conjunctive proposition is one which asserts that two alternatives cannot be true at the same time. (It is possible for both alternatives to be false.)

Ex. You cannot be in Manila and Baguio at the same time.

RULE FOR CONJUNCTIVE

Affirm one alternant in the minor premise and deny the other in the proposition. (Opposite of Rule for Broad Disjunctive)

You cannot smoke and stay in this room at the same time.But you want to stay in this room.Therefore, you cannot smoke.

You cannot smoke and stay in this room at the same time.But you do not want to smoke.Therefore, you can stay in this room.

Analyze each of the following hypothetical syllogisms. State its kind and whether it Is valid or invalid.

Either the witness is telling the truth or he is lying.But he is not telling the truth.Therefore, he is lying.

You are poor in Phil. History if you do not know what happened in Kawit, Cavite on June 12, 1898.You are poor in Philippine History.Therefore, you do not know what happened in Kawit, Cavite on June 12, 1898.

Having a healthy body entails that one must have a balanced diet.Lyndon has a healthy body.Therefore, he maintains a balanced diet.

Stevenson cannot plant vegetables and at the same time have chickens in the yard.But Stevenson decided to plant vegetables.Therefore, he will not have chickens in the yard.

Moises must write either his address or telephone number or both.He has written his address.Therefore, he must not write his telephone number.