Mathematics
Easy

Question

# Which law of deductive reasoning is being used, if any?If a triangle is equilateral, then all three sides are congruent.If all the sides of a triangle are congruent, then the angles opposite them are congruent.Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.

## Law of Detachment    Law of Syllogism    Law of the Contrapositive    Not valid Hint:

## The correct answer is: Law of Syllogism

### In the question it is given that,1) If a triangle is equilateral, then all three sides are congruent.2) If all the sides of a triangle are congruent, then the angles opposite them are congruent.3) Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.Here, we have to determine the law which the above statements obey.Let statement (1) be p, statement (2) be q and statement (3) be r.From the given statement we can say that p equals to q and r the conclusion drawn from p and q.So, the statement (3) is true for statement (1) and (2).Thus, the above statements obey the Law of Detachment.Therefore, the correct option is Law of Detachment.

In Law of Syllogism if a statement p equals q and if q equals r, then p equals r whereas in Law of Detachment if a statement p equals q where p is true then q is also true.

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