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Report in math (conjunctions and disjunctions)

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Report in math (conjunctions and disjunctions)

1. 1. Connectives are often used to join two simple statements are and,or, if … .then, if and only if. Two simple statements joined by the word “and is called a conjunction. The symbol “^” is used to represent the word “and”.
2. 2. Let p and q be simple statements. p: The number 3 is an even integer q: The number 7 is prime.Then the following in conjunction symbols: The number 3 is an even integer and the number 7 is prime. P ^ Q P Q P^Q The conjunction is a true statement if only both parts are true statements. Since p is false T T T statement, the conjunction is false. The T F F conjunction is usually expressed as and, F T F however, it can also be expressed as but, F F F however or nevertheless.
3. 3. Examples: Consider the following statements.a. Albay is in Bicol and 5+5=10b. Albay is in Bicol and 5+5=11c. Albay is in Laguna and 5+5=10d. Albay is in Laguna and 5+5=12Solution: Only statement a is true. Each of the other statement is false sinceat least one of its simple statements is false.
4. 4. Another ExampleGiven the truth values of p and q, state the truth value of theindicated statement.a. p true, q false; ~p ^ q b. p false, q false ~(~p ^ ~q)Solution:A. P Q ~P ~P ^ Q T F F FB. P Q ~P ~Q ~P ^ Q ~(~P ^ Q~) F F T T T F
5. 5. Check Your UnderstandingWhich statement is true?1. Chocolate Hills is in Bohol and 2 – 4 = 02. Chocolate Hills is in Iloilo and 2 – 4 = -23. Chocolate Hills is in Bohol and 2 – 4 = -2Given the truth values of p and q, state the truth values of theindicated statements4. p true, q true; p ^ ~q 6. p false, q false; ~(p ^ q)5. p true, q false; ~p ^ q 7. p false; q true; ~(~p ^ q)
6. 6. Two simple statements joined by the word “or” is called adisjunction. The symbol “v” is used to represent the word “or”.
7. 7. The disjunction of statements p and q giben in the previous page is The number 3 is an even integer and the number 7 is prime. P v Q P Q P^Q The above statement is true when at least one of the parts is true. Since q is true, even though T T T p is false, p v q is true. T F T The truth table for disjunction is given at the F T T right. F F F
8. 8. Examples: Consider the following statements.a. Albay is in Bicol or 5+5=10b. Albay is in Bicol or 5+5=11c. Albay is in Laguna or 5+5=10d. Albay is in Laguna or 5+5=12Solution: Only statement d is false. Each of the other statement is true sinceat least one of its simple statements is true.
9. 9. Another example Let p and q be statements given by:P: Triangle ABC has three sides.Q: Triangle ABC has sides of the same length.Triangle ABC has three sides Triangle ABC has sides of the same lengthWrite the following in symbolic form.a. Triangle ABC has three sides and its sides are of the same length.b. Triangle ABC has three sides or its sides are of the same length.c. Triangle ABC has three sides and its sides are not of the same length.d. It is no true that triangle ABC has three sides and its sides are of the same length.
10. 10. Another example: Write the following compound statements in terms of the givenstatements and give the truth value of the statementP: 6 is even Q: 9 < 5a. p ^ qb. p v qc. p ^ ~qd. ~p v q
11. 11. Check Your UnderstandingWrite the following compound statements in terms of the given simplestatements and give the truth value of the statement. M: 4 + 2 = 42 N: 4 x 2 > 5 O: 7 – 2 <01. M ^ N2. ~N V O3. M V O4. ~M ^ O