Logical Reasoning · Form 4
How 'and', 'or' and 'not' change truth
Negation ('not') flips a statement's truth value. Joining two statements with 'and' gives a true result only when both parts are true, while 'or' gives a true result when at least one part is true.
Negation turns true into false
Putting 'not' into a statement reverses its truth value. If 'Eight is an even number' is true, then 'Eight is not an even number' is false, and the reverse holds too.
Negation never leaves the truth value unchanged, it always swaps it.
'And' needs both; 'or' needs just one
A statement joined by 'and' is true only when every part is true, so '6 is even and 6 > 10' is false because the second part fails. A statement joined by 'or' is true as long as at least one part is true, so '6 is even or 6 > 10' is true on the strength of the first part alone.
Recognising which connective governs the sentence tells you what has to be checked.
Where students slip
In everyday speech 'or' often means one or the other but not both; in mathematics 'or' is inclusive, so it stays true even when both parts are true. The other common slip is negating only half of a compound sentence, the whole statement has to be handled, not just the first phrase.
Reading slowly to see which connective is in charge saves marks that are otherwise easy to lose.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I work out the truth value of a combined statement using "and"?
An "and" statement (conjunction) is true only when both parts are true individually, if even one part is false, the whole combined statement is false. For example, "6 is even and 6 is a multiple of 3" is true, since both parts hold.
Why is an "or" statement true even when only one part is true?
In SPM logical reasoning, "or" (disjunction) is inclusive: it's true whenever at least one part is true, and it's false only when both parts are false. This trips students who expect "or" to need exactly one part true, like everyday speech.
What's a common error when negating a statement with "not"?
Students often negate only part of the sentence or change its meaning instead of flipping its truth value exactly. "Not all numbers are even" negates "all numbers are even" it should mean "at least one number is not even", not "no numbers are even".