foundations of mathematical logic

Introduction - The study of logic through the use of mathematical symbols is called Mathematical Logic. Mathematical logic is also known as Symbolic Logic or Boolean Logic..

There are digital circuits which either allow a signal to pass through or stop it. The circuits other wise called as gate allows the signal to pass only when some logical condition are satisfied. Under such condition the circuits are called logic gates. They are building b..

Logic Gates - There are digital circuits which either allow a signal to pass through or stop it. The circuits other wise called as gate allows the signal to pass only when some logical condition are satisfied. Under such condition the circuits are called logic gates. T..

Two propositions (simple or compound) are said to be logically equivalent if they have identical truth values. If p is logically equivalent to q, we denote p q. We have already constructed the truth table of (~p) q in earlier class. Recall the same truth table. Truth Table fo..

Summary - - A sentence is a statement if it is either true or false, but not both. - The truth and falsity of a statement is its truth value. - A truth table indicates the truth values of a number of statements and their compound statements in a compact form. - If there are n statements, then there..

Two compound propositions p and q are said to be logically equivalent, if their truth values are same for each different combinations of the truth values of the components involved in them. If p and q are logically equivalent, then it is represented by p..

Two compound propositions p and q are said to be logically equivalent, if their truth values are same for each different combinations of the truth values of the components involved in them. If p and q are logically equivalent, then it is represented by p ..

Normally propositions are joined by 'OR', 'AND', 'NOT', 'IF .. THEN..' and 'IF AND ONLY IF' called the logical connectives . They are symbolised as follows: If two or more statements are combined by the use of words like 'AND', 'OR', 'IF AND ONLY IF ', then the resulting statement is ..

Let us refer to a circuit consisting of two switches p and q connected in parallel with a lamp and battery as shown in figure. In this case, the lamp will glow if and only if at least one of the switches is closed. In binary language we say the switch will glow if at least one of the values of p..

Venn diagrams are used very frequently on problems of set theory. Venn diagrams can also be used for deciding the truthfulness of statement..