MMW- WEEK 17- CONDITIONAL STATEMENTS.pptx

This PPT discusses about logical statement and different types of operations on logical statement. This will also guide you in determining the truth values using truth table. Furthermore, this includes the conditional and biconditional statement, and will shows the other form of conditional statement.

1. ERWIN A. MARIANO,MAED-MATH [email protected] MATHEMATICS IN THE MODERN WORLD GEC 004

2. Differentiate simple and compound logical statement. Familiarize with the logical connectives and symbols Give the truth values using truth tables GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements OBJECTIVES

3. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENT A statement (or proposition ) is a declarative sentence which is either true or false, but not both. Determine whether each sentence is a statement. Manila is in the Philippines. How are you? 3 is a prime number x + 4 = 15

4. Simple Statement- is a statement that conveys a single idea. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENT Compound Statement- is a statement that conveys two or more ideas p: Today is Sunday. r: Prof. Mariano is handsome. q: I love Mathematics in the Modern World. s: I am going to the basketball game.

5. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENT Type of Statement Connective Statement Symbolic Form Negation not not p Conjunction And p and q Disjunction Or p or q Conditional If… then If p, then q. Biconditional If and only if p if and only if q Type of Statement Connective Statement Symbolic Form Negation not not p Conjunction And p and q Disjunction Or p or q Conditional If… then If p, then q. Biconditional If and only if p if and only if q Truth Table- shows the truth value of a compound statement for all possible truth value of its simple statements.

6. Consider the following statement: GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENT Today is Sunday and Prof. Mariano is handsome. Write the following compound statements in symbolic form. p: Today is Sunday. r: Prof. Mariano is handsome. q: I love Mathematics in the Modern World. s: I am going to the basketball game. 2. I love MMW or I am not going to the basketball game. 3. If today is Sunday, then I am not going to the basketball game.

7. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENT p: Today is Sunday. r: Prof. Mariano is handsome. q: I love Mathematics in the Modern World. s: I am going to the basketball game. 5. If Prof. Mariano is not handsome, then I don’t love Mathematics in the Modern World. 6. Today is Sunday if and only if Prof.Mariano is handsome. 7. I’m not going to the basketball game if and only if today is not Sunday.

8. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENT p: Today is Sunday. r: It is raining. q: I will take a bath. s: I will not brush my teeth. p r q q (p (   Given the following statement. Translate each of the following symbols

9. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements CONJUNCTION The conjunction of the statement p and q is the compound statement “p and q.” Symbolically, p  q , where  is the symbol for “ and .” Property 1: If p is true and q is true, then p  q is true; otherwise p  q is false. Meaning, the conjunction of two statements is true only if each statement is true. p q p  q T T F F T F T F T F F F

10. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements DISJUNCTION The disjunction of the statement p, q is the compound statement “p or q.” Symbolically, p  q , where  is the symbol for “ or . ” Property 2: If p is true or q is true or if both p and q are true, then p  q is true; otherwise p  q is false. Meaning, the disjunction of two statements is false only if each statement is false. p q p  q T T F F T F T F T T T F

11. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements CONDITIONAL STATEMENT The conditional (or implication ) of the statement p and q is the compound statement “if p then q.” Symbolically, p  q , where  is the symbol for “ if then .” p is called hypothesis (or antecedent or premise) and q is called conclusion (or consequent or consequence). Property 4: The conditional statement p  q is false only when p is true and q is false; otherwise p  q is true. Meaning p  q states that a true statement cannot imply a false statement. p q p  q T T F F T F T F T F T T

12. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements CONDITIONAL STATEMENT If p, then q. Every p is a q. If p, q. q, if p p only if q. q provided that p. p implies q. q is a necessary condition for p. Not p or q. p is a sufficient condition for q. Common Forms of p   Every square is a rectangle. If a figure is a square , then it is a rectangle .

13. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENTS RELATED TO THE CONDITIONAL STATEMENT Converse Inverse Contrapositive The Converse of p is formed by interchanging the antecedent p and the consequent q. 2. The Inverse of p is formed by negating the antecedent p and negating the consequent q. 3. The Contrapositive of p is formed by negating both the antecedent p and the consequent q and interchanging these negated statements.  

14. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENTS RELATED TO THE CONDITIONAL STATEMENT CONDITIONAL CONVERSE INVERSE CONTRAPOSITIVE p q p q p q T T T T T T T F F T T F F T T F F T F F T T T T CONDITIONAL CONVERSE INVERSE CONTRAPOSITIVE p q T T T T T T T F F T T F F T T F F T F F T T T T

15. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional statements -The Conditional and Related Statements STATEMENTS RELATED TO THE CONDITIONAL STATEMENT Every square is a rectangle. Conditional: Converse: Inverse: Contrapositive: If a figure is a square, then it is rectangle If a figure is a rectangle, then it is a square. If a figure is a not a square, then it is not a rectangle. If a figure is a not rectangle, then it is not a square.

16. GEC 004 MATHEMATICS IN THE MODERN WORLD SECTION 2. MATHEMATICS AS A TOOL LOGIC -The conditional and Biconditional Statements -The Conditional and Related Statements STATEMENTS RELATED TO THE CONDITIONAL STATEMENT The sum of the measures of two complementary angles is 90 degrees. Conditional: Converse: Inverse: Contrapositive: If two angles are complementary, then the sum of the measures is 90 degrees. If the sum of the measures of two angles is 90 degrees, then they are complementary If two angles are not complementary, then the sum of the measures is not 90 degrees If the sum of the measures of two angles is not 90 degrees, then they are not complementary

17. GEC 004 MATHEMATICS IN THE MODERN WORLD