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Truth Tables
A table is indicating the truth values of one or more statements is called a truth table..
Compound statements and Truth table
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..
Table 2 - Truth table for p and q
The 'AND' operation can be defined on the set of bits {0, 1} as follows 1 . 1 = 1, 1 . 0 = 0, 0.1 = 0, 0.0 =..
The 'AND' operation can be defined on the set of bits {0, 1} as follows 1 . 1 = 1, 1 . 0 = 0, 0.1 = 0, 0.0 =..Amongst a group of patients who complained of severe body pain, some w..
Amongst a group of patients who complained of severe body pain, some were given a new analgesic on trial and some were given a placebo. They were later asked whether the pain relievers were effective. The results were presented in the following table. Pain relieved Pain continues Took analgesi..
Logical 'NOT' Operation
This operation has one input and one output. Table 7 represents truth table for NOT operati..
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 stateme..
Conditional and Biconditional Statements
Conditional and Biconditional Statements - It is already mentioned in earlier classes that compound statements of different propositions can be obtained by conjunction, disjunction and negation of propositions. We just recall these three basic logical connectivities and their truth t..
Negation
Let p be any proposition. The proposition "not p" is called the negation of p. It is denoted by ~p. [The negation of p is false if p is true and the negation of p is true if p is false] Following is the truth table for ~p..
Let p be any proposition. The proposition "not p" is called the negation of p. It is denoted by ~p. [The negation of p is false if p is true and the negation of p is true if p is false] Following is the truth table for ~p..Logical Equivalence
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 h..
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 h..Conjunction
If p and q are two propositions, then the compound proposition "p and q" is known as conjunction of the proposition. It is denoted by [The conjunction of two propositions p and q is true if both p and q are true and in all other cases it is false] The truth table of p q is ..
If p and q are two propositions, then the compound proposition "p and q" is known as conjunction of the proposition. It is denoted by [The conjunction of two propositions p and q is true if both p and q are true and in all other cases it is false] The truth table of p q is ..See what our Users say :
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