| Date | May 2012 | Marks available | 2 | Reference code | 12M.1.sl.TZ1.6 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | State | Question number | 6 | Adapted from | N/A |
Question
Consider the statements
p : The numbers x and y are both even.
q : The sum of x and y is an even number.
Write down, in words, the statement p \(\Rightarrow\) q.
Write down, in words, the inverse of the statement p \(\Rightarrow\) q.
State whether the inverse of the statement p \( \Rightarrow \) q is always true. Justify your answer.
Markscheme
If (both) the numbers x and y are even (then) the sum of x and y is an even number. (A1)(A1) (C2)
Note: Award (A1) for If…(then), (A1) for the correct statements in the correct order.
[2 marks]
If (both) the numbers x and y are not even (then) the sum of x and y is not an even number. (A1)(A1) (C2)
Notes: Award (A1) for If…(then), (A1) for the correct not p, and not q in the correct order. Accept the word odd for the phrase “not even”.
[2 marks]
The inverse of a statement is not (necessarily) true, because two odd (not even) numbers, always have an even sum. (A1)(R1)(ft) (C2)
Notes: Award (A1)(R1) if a specific counter example given instead of a reason stated in general terms, e.g. the inverse is not true because, 5 and 7 have an even sum. Do not award (A1)(R0). Follow through from their statement in part (b).
[2 marks]
Examiners report
Although a few candidates did not seem to understand the meaning of the \(\Rightarrow\) symbol, many scored a minimum of two marks on the first two parts of the question. Indeed, many correct statements were seen in part (a). Many candidates however confused converse with inverse in part (b) resulting in the incorrect statement "if the sum of x and y are both even then the numbers x and y are both even" appearing on many scripts earning (M1)(A0). Despite this incorrect compound statement, many candidates recovered with correct reasoning in part (c) from their correct (or incorrect) statement in part (b). Candidate's responses to part (c) of the question should have been given in the context of the question set and those that simply inferred their answer from truth tables only, earned no marks.
Although a few candidates did not seem to understand the meaning of the \(\Rightarrow\) symbol, many scored a minimum of two marks on the first two parts of the question. Indeed, many correct statements were seen in part (a). Many candidates however confused converse with inverse in part (b) resulting in the incorrect statement "if the sum of x and y are both even then the numbers x and y are both even" appearing on many scripts earning (M1)(A0). Despite this incorrect compound statement, many candidates recovered with correct reasoning in part (c) from their correct (or incorrect) statement in part (b). Candidate's responses to part (c) of the question should have been given in the context of the question set and those that simply inferred their answer from truth tables only, earned no marks.
Although a few candidates did not seem to understand the meaning of the \(\Rightarrow\) symbol, many scored a minimum of two marks on the first two parts of the question. Indeed, many correct statements were seen in part (a). Many candidates however confused converse with inverse in part (b) resulting in the incorrect statement "if the sum of x and y are both even then the numbers x and y are both even" appearing on many scripts earning (M1)(A0). Despite this incorrect compound statement, many candidates recovered with correct reasoning in part (c) from their correct (or incorrect) statement in part (b). Candidate's responses to part (c) of the question should have been given in the context of the question set and those that simply inferred their answer from truth tables only, earned no marks.
