# Deductive Reasoning

### Study Tool

## 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.

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.

## For Example

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