College Math

College Math Study Guide

6.3 Conjunction The symbol for AND (∧) denotes conjunction and is written as a ∧ b. It should be noted that the connective ‘ but’ is identical to connective ‘ and’ . For instance, if we are given the above two statements as: Your bracelet has diamonds but I don’t like its design will be written symbolically as a ∧ ~b (that is, a is true and b is not true). 6.4 Disjunction The symbol for OR (∨) denotes disjunction and is written as a ∨ b. It should be noted that the connective OR has an inclusive meaning. That is, Emily will go to see a movie or will go for basketball class will be interpreted as Emily will wither go to see a movie or will go for basketball class, or do both. 6.5 Parentheses Parentheses should be dealt with due care whenever we wish to form any statement in symbolic form. Suppose we are given this statement: I have to conduct a search for web pages containing “journal” or “articles”, then I have to search for web pages containing “scholarly papers”. To write this sentence symbolically, split this sentence into simple statements and then apply different logic notations. a = I search for web pages containing “journal” b = I search for web pages containing “articles” c = I search for web pages containing “scholar papers” Now, use the disjunction and conditional symbols: (a ∨ b) → c The use of parentheses is very important here. If we miss the parentheses, then the symbolic representation would have been a ∨ b → c, and this would have meant that I search on web for pages containing “journal” or if I search on web for pages containing “articles”, then I search for those containing “scholar papers”. This statement is entirely different from the one given above, and hence, the importance of parentheses needs to be considered carefully.

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