# Deductive Reasoning

## Definition

Deductive reasoning is a logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true. (WhatIs.com)

## In Mathematics

If A = B and B = C, then A = C.

Since all squares are rectangles, and all rectangles have four sides, so all squares have four sides.

All numbers ending in 0 or 5 are divisible by 5. The number 35 ends with a 5, so it is divisible by 5.

Acute angles are less than 90 degrees and this angle is 40 degrees so this angle is acute.

## In Science

All noble gases are stable and helium is a noble gas, so helium is stable.

The Earth is a planet, and all planets orbit a sun, therefore the Earth orbits a sun.

Cacti are plants and all plants perform photosynthesis; therefore, cacti perform photosynthesis.

## In Life

If Dennis misses work and at work there is a party, then Dennis will miss the party.

William is a bachelor, all bachelors are single; hence William is single.

"Deductive reasoning is one of the most valuable skills a student can have when working to prove a mathematical theorem, analyzing literature, or taking a standardized test. Deductive reasoning is what allows a student to discover the correct answer to a question he or she may not have been anticipating. At its most basic level, it is simply applying larger truths and over-arching facts to smaller questions to arrive at the logical answers." (Yahoo.com)
As opposed to inductive reasoning, deductive reasoning has the advantages of certainty and objectivity. (RationalWiki.org)
For deductive reasoning to be successful, the logic derived from it must be true and valid. Therefore, if it is not, even a valid deductive argument could be false.

## For Example

All politicians are liars, all vehicle salespersons are liars, therefore all politicians are vehicle salespersons.