Quarter 2 Logic Module, Cheat Sheet of English

Download Quarter 2 Logic Module and more Cheat Sheet English in PDF only on Docsity! STUDENT ACTIVITY WORKSHEET QUARTER 2 - WEEK 7 EXAMPLES for ACTIVITY 1 and ACTIVITY 2 Subject Area and Grade Level : GENERAL MATHEMATICS / GRADE 11 Learning Competency (MELCs) : 1. Illustrates and symbolizes propositions 2. Distinguishes between simple and compound proposition. 3. Performs the different types of operations on propositions. Subject Matter : Logic References: General Mathematics Learner’s Material pp.240-244 General Mathematics by L. Dimasuay pp. 170-174 General Mathematics by O.A. Oronce pp.268-272 Examples of Proposition and Not a Proposition. Decide whether each of the following is a proposition or is not a proposition. 1. Rowena is passing in Mathematics. Proposition 2. Pass the paper and then leave the room. Not a proposition 3. December 7, 1953 was a Monday. Proposition 4. When will you submit your project? Not a proposition 5. 5 + 3 = 8 and 12 -7 = 5. Proposition 6. The number 4 is even and less than 12. Proposition 7. Malolos is the Capital of Bulacan. Proposition 8. How old are you? Not a proposition 9. Open your eyes. Not a proposition 10. Aron’s solution is incorrect. Proposition Definition of Terms with examples: Conjunction: Two simple propositions connected using the word and. Example 1: “Today is Friday and tomorrow is Saturday.” (Sometimes the word “but” will be used in place of “and” in a given sentence.) Example 2: “Roel was on time, but Tom was late.” “Roel was on time and Tom was late.” Points to Remember A proposition is a declarative sentence that is either true or false but not both. It is denoted by a small letter. The truth value of a proposition is denoted as T if it is true and F if it is false. A simple proposition is one which cannot be broken down further into component propositions and is denoted by a small letter(i.e. p, q, r, etc.) A compound proposition is composed of two or more simple propositions joined together by connective words or logical operators namely “not”, “and”, “or”, “if…then”, and “if and only If”. Disjunction: Two simple propositions that are connected using the word “or”. Example 1: “I will pass the Math exam ’or’ I will be promoted.” Conditional: Two simple propositions that are connected using the words if… then. Example 1: “If you will recite the poem, then you will pass the oral examination” Note: The statement between the if and then is called the antecedent of the conditional. The sentence that follows then is called consequent. Example 2: If you will recite the poem, you will pass the oral examination; or You will pass the oral examination if you will recite the poem. In (a), then was omitted but it is understood to be there. In (b), the two parts are switched around and then was also omitted. Nonetheless, both (a) and (b) are conditionals. Biconditional: Conjuction of two conditional statements where the antecedent and consequent of the first statement have been switched in the second statement. Example 1: If two sides of a triangle are congruent, then the angle opposite them are congruent, and if two angles of a triangle are congruent, then the sides opposite them are congruent. Note: The sentence above is usually stated as “Two sides of a triangle are congruent if and only if two angles opposite them are congruent.” Negation: The negation of a given statement is a statement that is false whenever the given statement is true, and true whenever the given statement is false. The negation can be obtained by inserting the word not in the given statement or by prefixing it with phrases such as “it is not the case that…” Example 1: The negation of the statement “Herbert is good” can be written as: “Herbert is not good.” or “It is not the case that Herbert is good.” Example 2: Give the negation of the statement “Her aunt’s name is Lucia. By inserting not in the statement: “Her aunt’s name is not Lucia.” By prefixing the phrase “It is not the case that” “It is not the case that her aunt’s name is Lucia.” The abbreviation for if and only if is iff.