Logical Reasoning · 3.1.3
Truth value of compound statements
This standard asks students to combine two simple statements using 'and' or 'or' to form a compound statement, then decide if it is true or false. An 'and' statement is true only when both parts are true; an 'or' statement is true when at least one part is true.
The official learning standard (3.1.3)
“Determine the truth value of a compound statement. A compound statement is a combination of two statements using "and" or "or".”
What it means
This standard asks students to combine two simple statements using 'and' or 'or' to form a compound statement, then decide if it is true or false. An 'and' statement is true only when both parts are true; an 'or' statement is true when at least one part is true.
How it is examined
Paper 1 typically gives a compound statement and asks students to state whether it is true or false, or to identify the individual statements that form it. Paper 2 may embed compound statements within larger reasoning questions, requiring students to justify the truth value with reference to both component statements.
Worked example
Given the statements p: 6 is an even number, q: 6 is a multiple of 4, determine the truth value of 'p and q' and 'p or q'.
- p: 6 is an even number, TRUE
- q: 6 is a multiple of 4, FALSE (6 ÷ 4 = 1.5)
- 'p and q' is true only if both p and q are true; since q is false, 'p and q' is FALSE
- 'p or q' is true if at least one is true; since p is true, 'p or q' is TRUE
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What's the difference between 'and' and 'or' in a compound statement?
'And' (conjunction) needs both statements to be true for the whole thing to be true. 'Or' (disjunction) only needs at least one statement to be true.
So 'and' is stricter, and 'or' is more easily satisfied.
Can a compound statement combine more than two statements?
At SPM level, compound statements are usually formed from exactly two simple statements joined by 'and' or 'or', following the DSKP scope for this standard.
How do I quickly check the truth value without writing a full table?
Determine the truth value of each simple statement first. For 'and', it is false if either part is false.
For 'or', it is true if either part is true. This shortcut avoids needing a full truth table.