Logical Reasoning · 3.2.2
Validity of deductive arguments
A deductive argument is valid when its conclusion must be true whenever all its premises are true, based on its logical structure. A valid argument is further called sound only when its premises are actually true.
Students learn to test forms such as syllogisms for validity and soundness.
The official learning standard (3.2.2)
“Determine and justify the validity of a deductive argument hence determine whether the valid argument is sound. Various forms of deductive arguments need to be involved including:”
What it means
A deductive argument is valid when its conclusion must be true whenever all its premises are true, based on its logical structure. A valid argument is further called sound only when its premises are actually true.
Students learn to test forms such as syllogisms for validity and soundness.
How it is examined
Paper 1 may test recognition of valid argument forms, such as syllogisms involving 'all', 'some' or implications. Paper 2 typically presents a full deductive argument with stated premises and asks students to determine and justify whether it is valid, and separately whether it is sound.
Worked example
Determine whether the following deductive argument is valid, and whether it is sound: Premise 1: All multiples of 6 are multiples of 3. Premise 2: 18 is a multiple of 6.
Conclusion: 18 is a multiple of 3.
- Check the logical structure: if all multiples of 6 are multiples of 3, and 18 is a multiple of 6, the conclusion that 18 is a multiple of 3 must follow, the argument is valid
- Check Premise 1: all multiples of 6 are indeed multiples of 3 (since 6 = 2 × 3), TRUE
- Check Premise 2: 18 = 6 × 3, so 18 is a multiple of 6, TRUE
- Since the argument is valid and both premises are true, the argument is sound
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What's the difference between a valid argument and a sound argument?
Validity is about logical structure, the conclusion must follow if the premises are true, regardless of whether they actually are. Soundness requires both validity and that the premises are actually true.
So a sound argument is always valid, but a valid argument isn't always sound.
Can a valid argument have a false conclusion?
Yes, if at least one premise is false. Validity only ensures the conclusion follows logically from the premises, it does not ensure the premises or conclusion are true in reality.
That's why soundness needs true premises too.
How do I check if a deductive argument is valid?
Check whether the conclusion must be true whenever all the premises are assumed true, based purely on the logical structure connecting them, such as through 'all', 'some', or implication forms, not by checking real-world truth at this stage.