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Application of sets
The theory of finite sets is, arguably, a definition of Combinatorics. In particular, certain combinatorial topics (e.g. Ramsey theory) have important direct analogues in "combinatorial" set theory. Since Axiomatic Set Theory is often used to construct the natural numbers (satisfying the Pean..
Logic Gates
The basic building blocks for a complex digital system are known as logic gates. A gate is a simple electronic circuit or device that performs logical functions. It has one or more inputs and one output gate and are also called binary logic gates, as 1 and 0 are the i..
Mathematical Logic Introduction
Introduction - Logic is the study and analysis of valid arguments. The arguments are in the form of statements or propositions, which are either true or false, but not both. There are also some statements, which appear to be true and false at the same time. They are called paradoxes. The ..
Logical Equivalence and Duality
Logical Equivalence and Duality - 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 ..
Use of Venn diagrams in Logic
Use of Venn diagrams in Logic - Venn diagrams are used very frequently on problems of set theory. Venn diagrams can also be used for deciding the truthfulness of statemen..
Logical connectives and compound statements
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 ..
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 ..Logical 'OR' operation
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..
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..Use of Venn diagrams in Logic
Venn diagrams are used very frequently on problems of set theory. Venn diagrams can also be used for deciding the truthfulness of statement..
Application of Logic in solving simple problems
Argument - An argument is a statement which assets that a given set of n compound statements p 1 ,p 2 ,..........p n yield another compound statement Q. This is denoted by where p 1 ,p 2 ,..........p n are called hypotheses or premises or assumptions. The compound statement Q is called the conclusi..
Argument - An argument is a statement which assets that a given set of n compound statements p 1 ,p 2 ,..........p n yield another compound statement Q. This is denoted by where p 1 ,p 2 ,..........p n are called hypotheses or premises or assumptions. The compound statement Q is called the conclusi..Select the correct statement(s). I. Deductive reasoning arrives at a v..
Select the correct statement(s). I. Deductive reasoning arrives at a valid conclusion by logical reasoning based on the available facts. II. Deductive reasoning is the only method to prove theorems. III. In geometry, postulates and properties are accepted as true and these are used in ded..
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