Rapid Revision · Logical Reasoning
Given statements like 'All A are B', decide which conclusions MUST follow. Venn diagrams turn word logic into shapes you can read straight off.
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All A are B
A fully inside B => 'some B are A' holds, but NOT 'all B are A'
Some A are B
A and B overlap => symmetric, so 'some B are A' also holds
No A are B
A and B disjoint => symmetric, so 'no B are A' also holds
Validity rule
a conclusion follows only if it is true in EVERY valid diagram
6 cards, each one idea: what it is, a worked example, and the trap to dodge.
Each statement is a relationship between two circles. Draw the guaranteed case first, then ask whether any other arrangement is also allowed.
'All pens are books; all books are red' => pens inside books inside red => 'all pens are red' follows.
The exam asks what MUST be true. If you can draw even one valid diagram where a conclusion fails, that conclusion does not follow.
Trap: 'Some A are B' does NOT give 'some A are not B'. The overlap could be total.
'Some A are B' is symmetric, so 'some B are A' also holds. 'All A are B' gives 'some B are A' but never 'all B are A'.
All cats are animals => some animals are cats (true); all animals are cats (false).
'No A are B' means the circles are disjoint, and it is symmetric: 'no B are A' also holds. Combine it carefully with 'all' and 'some'.
No A are B; all C are A => no C are B follows.
When two conclusions look contradictory, neither is individually certain, but together they cover all cases, the answer is 'either I or II follows'.
'Some A are B' and 'no A are B' as a pair exhaust every possibility.
Trap: Either-or applies only when the two conclusions are complementary AND jointly exhaustive.
For three statements, draw one combined diagram satisfying all three, then test each conclusion against it and any alternative you can construct.
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