Which answers are examples of the law of syllogism? select each correct answer. if two numbers are even then their sum is even. ten and 12 are even numbers. the sum of 10 and 12 is even. if the lengths of the sides of a triangle are equal, the triangle is an equilateral triangle. if a triangle is equilateral, each angle of the triangle measures 60°. therefore, if the lengths of the sides of a triangle are equal, each angle of the triangle measures 60°. if the dog belongs to mike, the dog is a beagle. jake is mike’s dog. therefore, jake is a beagle. if a student sells 10 boxes of candy, the student will get to go on the class field trip. if there is a class field trip, it will be to the aquarium. therefore, if a student sells 10 boxes of candy, the student will get to go to the aquarium.

A syllogism is a form of logical reasoning that joins two or more premises to arrive at a conclusion. They include a major premise and a minor premise. In comparison, the law of detachment is when there are two premises that are accepted as true and are used to reach a conclusion (if p, then q).

The bolded statments show the law of syllogism (the answer to the question), while the unbolded statements are examples of the law of detachment.

Law of syllogism

If the lengths of the sides of a triangle are equal, the triangle is an equilateral triangle. If a triangle is equilateral, each angle of the triangle measures 60°. Therefore, if the lengths of the sides of a triangle are equal, each angle of the triangle measures 60°.

If a student sells 10 boxes of candy, the student will get to go on the class field trip. If there is a class field trip, it will be to the aquarium. Therefore, if a student sells 10 boxes of candy, the student will get to go to the aquarium.

Law of detachment

If two numbers are even then their sum is even. Ten and 12 are even numbers. The sum of 10 and 12 is even.

If the dog belongs to Mike, the dog is a beagle. Jake is Mike’s dog. Therefore, Jake is a beagle.

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