1. IB Math Studies – Topic 3

2. Statements A statement – sentence or phrase precise mathematical meaning A statement/proposition has a truth value.

3. Practice 2 + 2 = 5 Make the tea. The moon is made of green cheese. 5 > 2 A week is consists of 5 days. Have a nice day! Is it snowing?

4. Compound Statements A compound statement is made up of simple statements joined together by connectives. ConnectiveDescriptionSymbol NOTNegation ANDConjunction ORInclusive disjunction ORExclusive disjunction IF…THENImplication

5. Negation The negation of a proposition is formed by putting words such as “not” or “do not.” The negation of a proposition p is “not p” and is written as ¬p.  For example:  p: It is Monday.  ¬p: It is not Monday.

6. Truth Tables A truth table shows how the values of a set of propositions affect the values of other propositions. A truth table for negation p¬ p TF FT

7. Check your understanding Write negations of the following statements. The student is a council member. The student is not a council member.

8. Check your understanding Write negations of the following statements. She owns a mobile phone. She does not own a mobile phone.

9. Check your understanding Write negations of the following statements. n is a prime number n is not a prime number

10. Check your understanding Write negations of the following statements without using the word ‘not’. The word starts with a vowel. The word starts with a consonant.

11. Check your understanding Write negations of the following statements without using the word ‘not’. There is an even number of pages in this book.. There is an odd number of pages in this book.

12. Check your understanding In these statements, is q the negation of p? if not, say why it is not the negation. p: Mario obtained the highest mark on the test. q: Mario obtained the lowest mark on the test. No. The negation of p would be that Mario obtained any mark other than the highest.

13. Check your understanding In these statements, is q the negation of p? if not, say why it is not the negation. p: This test is difficult. q: This test is easy. No. The test could be not difficult without being easy.

14. Check your understanding In these statements, is q the negation of p? if not, say why it is not the negation. p: Sahana scored more than 50% on the test. q: Sahana scored less than 50% o the test. No. Sahana could have scored 50% on the test.

15. Check your understanding In these statements, is q the negation of p? if not, say why it is not the negation. p: Richard is inside the classroom. q: Richard is outside the classroom. YES

16. Independent Practice Answer the questions on pages 387 – 388, #s 4-8.