(Total 4 marks) Paper 2 Style Questions 6. Let the propositions and be defined as: p, q r p: Matthew arrives home before six o’clock Matthew cooks dinner q: Jill washes the dishes r: (a) (i) Express the following statement in logical form. If Matthew arrives then he will cook dinner. home before six o’clock (1) (ii) Write the following logic statement in words.  q   r (1) (b) (i) Copy and complete the truth table below. (p (q [(p (q p q r   r     r p     r]  p p q q r q) r) q) r) T T T T T T F T T F T T T F F T F T T T F T F T F F T T F F F T (5) (ii) Explain the significance of the truth table above. (2) (Total 9 marks) 7. Let = {x : 1 < 17,  }. x x ≤ , and are the subsets of such that P Q R = {multiples of four}; P = {factors of 36}; Q = {square numbers}. R (a) List the elements of (i) (ii) P  Q  R. (2) (b) Describe in words the set  P Q. (1) (c) (i) Draw a Venn diagram to show the relationship between sets and P, Q R. (2) (ii) Write the elements of in the appropriate places on the Venn diagram. (3) (d) Let and be the statements p, q r is a multiple of four; p: x is a factor of 36; q: x is a square number. r: x
(Total 4 marks) Paper 2 Style Questions 6. Let the propositions p, q and r be defined as: p: Matthew arrives home before six o’clock q: Matthew cooks dinner r: Jill washes the dishes (a) (i) Express the following statement in logical form. If Matthew arrives home before six o’clock then he will cook dinner. (1) (ii) Write the following logic statement in words.  q   r (1) (b) (i) Copy and complete the truth table below. p q r p  q q  r r (p  q)  (q  r)  r p [(p  q)  (q  r)  r]  p T T T T T T F T T F T T T F F T F T T T F T F T F F T T F F F T (5) (ii) Explain the significance of the truth table above. (2) (Total 9 marks) 7. Let = {x : 1 ≤ x < 17, x  }. P , Q and R are the subsets of such that P = {multiples of four}; Q = {factors of 36}; R = {square numbers}. (a) List the elements of (i) (ii) P  Q  R. (2) (b) Describe in words the set P  Q. (1) (c) (i) Draw a Venn diagram to show the relationship between sets P, Q and R. (2) (ii) Write the elements of in the appropriate places on the Venn diagram. (3) (d) Let p, q and r be the statements p: x is a multiple of four; q: x is a factor of 36; r: x is a square number.