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Introduction |
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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. |
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Proposition or statement and Truth Value of a statement |
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A declarative sentence which is true or false but not both is called a proposition. Truth value is the truthfulness of statement. If a statement is true its truth value is T, if a statement is false then its truth value is F. |
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Use of Venn diagrams in Logic |
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Venn diagrams are used very frequently on problems of “set theory”. Venn diagrams can also be used for deciding the truthfulness of statements. |
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Compound statements and Truth table |
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If two or more statements are combined by the use of words like 'AND', 'OR', 'IF AND ONLY IF ', then the resulting statement is called a compound statement. A table is indicating the truth values of one or more statements is called a truth table. |
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Logical Equivalence and Duality |
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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 º
q. |
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Application of Logic in solving simple problems |
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An argument is a statement which assets that a given set of n compound statements p1,p2,..........pn yield another compound statement Q. |
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Summary |
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- 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 are 2n rows in the truth table.
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