Application of Logic in solving simple problems

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Argument

An argument is a statement which assets that a given set of n compound statements p₁,p₂,..........p_n yield another compound statement Q.

This is denoted by

where p₁,p₂,..........p_n are called hypotheses or premises or assumptions.

The compound statement Q is called the conclusion.

The argument p₁, p₂,...., p_n Q is defined to be true if Q is true whenever p₁,p₂,..........p_n are all true.

Otherwise, the argument is defined to be false.

A true argument is also called a valid argument.

Useful steps for solving problems:

Step i:

Identify the component statements in the given argument and denote these as p, q, r,……

Step ii:

Identify the assumptions and denote these as p₁,p₂,p₃....

Step iii:

Identify the conclusion as Q.

Step iv:

Express p₁,p₂,p₃...., Q in terms of p, q, r,……

Step v:

Find the truth values of p₁,p₂,p₃...., Q

Step vi:

If Q is true whenever p₁,p₂,p₃.... are all true, then the argument p₁, p₂,... Q is valid, otherwise it is invalid.