Only one of the statements in part(a) is true. Which one is it?

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1 M02/1/13 1. Consider the statement If a figure is a square, then it is a rhombus. or this statement, write in words (i) (ii) (iii) its converse; its inverse; its contrapositive. Only one of the statements in part is true. Which one is it? (i) (ii) (iii) (otal 8 marks) 1

2 N02/1/04 2. Consider the following statements. p: students work hard q: students will succeed Write the following proposition in symbols using p, q and logical connectives only. If students do not work hard, then they will not succeed. Complete the following truth table, relating to the statement made in part, and decide whether the statement is logically valid. p q (otal 8 marks) 2

3 M03/1/05 3. he following truth table contains two entries which are incorrect, one in column three and one in column four. Circle the two incorrect entries. ill in the two missing values in column five. Which one of the following words could you use to describe the statement represented by the values in the last column (number 6)? i. converse ii. iii. iv. tautology inverse contradiction v. contrapositive p q p q p p q (p q) ( p q) Answer:... (otal 8 marks) 3

4 N03/1/05 4. Consider two propositions p and q. Complete the truth table below for the compound proposition. (p q) ( p q) p q p q p q p q (p q) ( p q) (d) (f) (g) (e) (h) (otal 8 marks) 4

5 N03/1/14 5. Solve 2x + 3 = 5. Consider the logic statements. p: 2x + 3 = 5 q: x 2 = x he compound proposition 2x + 3 = 5 x 2 = x is given. true? Is this compound proposition (d) Write down the converse of this compound proposition. Give an example to show that the converse is false (d) (otal 8 marks) 5

6 M04/1/03 6. Let p and q be the statements: p: Sarah eats lots of carrots. q: Sarah can see well in the dark. Write the following statements in words. p q. p q. Write the following statement in symbolic form. If Sarah cannot see well in the dark, then she does not eat lots of carrots. (d) Is the statement in part the inverse, the converse or the contrapositive of the statement in part? (d)... (otal 8 marks) 6

7 N04/1/06 7. Consider the following logic statements: p: the train arrives on time q: I am late for school Write the expression p q as a logic statement. Write the following statement in logic symbols: "he train does not arrive on time and I am not late for school." Complete the following truth table. p q p q p q p q (d) Are the two compound propositions (p q) and ( p q) logically equivalent? (d)... (otal 8 marks) 7

8 N05/1/11 8. Complete the ruth able for the compound proposition (p q) (p q). p q q (p q) (p q) (p q) (p q) (otal 8 marks) 8

9 M06/1/04 9. Consider the statements p: he sun is shining. q: I am wearing my hat. Write down, in words, the meaning of q p. Complete the truth table. p q p q p Write down, in symbols, the converse of q p (otal 6 marks) 9

10 N06/1/ wo logic propositions are given p: Dany goes to the cinema q: Dany studies for the test Write in words the proposition p q. Given the statement s: If Dany goes to the cinema then Dany doesn t study for the test. (i) (ii) Write s in symbolic form. Write in symbolic form the contrapositive of part (i). (i)... (ii)... (otal 6 marks) 10

11 M07/1/ he truth table below shows the truth-values for the proposition p q p q p q p q p q p q p q p q Explain the distinction between the compound propositions, p q and p q. ill in the four missing truth-values on the table. State whether the proposition p q p q is a tautology, a contradiction or neither. (otal 6 marks) 11

12 N07/1/ You may choose from three courses on a lunchtime menu at a restaurant. s: you choose a salad, m: you choose a meat dish (main course), d: you choose a dessert. You choose a two course meal which must include a main course and either a salad or a dessert, but not both. Write the sentence above using logic symbols. Write in words s d. Complete the following truth table. s d s s d (otal 6 marks) 12

13 M08/1A/ Consider the following logic propositions: p: Sean is at school q: Sean is playing a game on his computer. Write in words, p q. Write in words, the converse of p q. Complete the following truth table for p q. p q q p q (otal 6 marks) 13

14 M08/1R/ (i) Complete the truth table below. p q p q (p q) p q p q (ii) State whether the compound propositions (p q) and p q are equivalent. Consider the following propositions. p: Amy eats sweets q: Amy goes swimming. (4) Write, in symbolic form, the following proposition. Amy either eats sweets or goes swimming, but not both. (ii) (otal 6 marks) 14

15 M03/2/A1(ii) 15. Consider each of the following statements: p: Alex is from Uruguay q: Alex is a scientist r: Alex plays the flute Write each of the following arguments in symbols: (i) If Alex is not a scientist then he is not from Uruguay. (ii) If Alex is a scientist, then he is either from Uruguay or plays the flute. (3) Write the following argument in words: r (q p) (3) Construct a truth table for the argument in part using the values below for p, q, r and r. est whether or not the argument is logically valid. p q r r (4) (otal 10 marks) 15

16 M05/2/3(i) 2. Let p stand for the proposition I will walk to school. Let q stand for the proposition the sun is shining. Write the following statements in symbolic logic form (i) (ii) If the sun is shining then I will walk to school. If I do not walk to school then the sun is not shining. (4) Write down, in words, the converse of the statement If the sun is shining then I will walk to school. (otal 6 marks) M05/2/3(ii) 3. Copy and complete the table below by filling in the three empty columns. p q p q p q p (p q) p (p q) p q What word is used to describe the argument (p q) p q? (3) (1) (otal 4 marks) 16

17 N05/2/2(ii) 4. Consider the following logic statements: p: x is a factor of 6 q: x is a factor of 24 Write p q in words. (1) Write the converse of p q. (1) State if the converse is true or false and give an example to justify your answer. (otal 4 marks) 17

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