Ch 1Mathematical Logic — Class 12 Mathematics, concept-first.

Mathematics is a subject built on precision, and that precision comes from proof. A proof, in turn, is only as good as the reasoning behind it — and the formal study of correct reasoning is what we ca…

In everyday language we use many kinds of sentences — questions, requests, exclamations, commands, and plain factual assertions. Logic singles out only the last kind for formal study.

Since a statement can only be true or false, we say it carries a truth value: the truth value is written as T when the statement is true, and F when the statement is false.

So far we have looked at single (simple) statements. In practice we very often build bigger statements out of smaller ones by joining them with connecting words like "and," "or," "if ...

In mathematical logic we abbreviate simple statements using single letters such as , , , ... — these are called statement letters.

Two statement patterns are compared not by how similar they look on paper, but by how they behave under every possible truth assignment.

Tautology, Contradiction and Contingency

A quantifier is a word that tells us how many members of a collection must satisfy a stated condition before the resulting sentence counts as true. Two quantifiers are used in mathematics.

Two statements built only from the connectives (or) and (and) — possibly together with the tautology and the contradiction — are called duals of one another if one can be obtained from the other by a…

Some compound statements have negations that deserve naming in their own right, because they let us rewrite 'not (A and B)' or 'not (A or B)' as a positive-looking statement instead of leaving a sitti…

Starting from a single implication , three related implications can be built by rearranging or negating its two parts: - is the converse of (the sides are swapped).

Four equivalences underpin most of the simplification work in this chapter. This section proves the first two with a single truth table and leaves the other two as a truth-table activity.

Every simplification in this chapter, from here on, is really just a chain of substitutions drawn from one fixed list of standard equivalences — the 'algebra of statements'.

The algebra of logical statements has a striking twin in electrical switching networks — an analogy first pointed out by Claude Shannon in 1930.

Now wire and side by side, each offering its own path to the lamp (a parallel connection), with for and for .

Sample papers and previous-year board questions for this subject.