Reasoning · Grade 6-1 Deductive Logic (1)
Problem
The example gives the pattern all A are B.
This is the same rule a Grade 5 student already uses about shapes: every square is a rectangle, so anything true of all rectangles is automatically true of every square. A syllogism is just that rule written out in three lines.
5.G.B.3Solve An Easier Related ProblemDraw it as two circles and a dot.
A nested-circle diagram makes 'must follow' visible: once the small circle is drawn inside the big one, no dot inside the small circle can escape the big one, so no counterexample can even be drawn.
5.G.B.4Draw A Venn DiagramDrawing the two premises as nested circles with a dot inside makes the conclusion impossible to escape.
If every A is a B, then anything true of all B is automatically true of every A, so the small circle inherits the big one's properties.
Being inside chains along: a dot inside the small circle is inside the big one too, so no counterexample can even be drawn.
Matching forwards, (1) yields the conclusion.
Once the two premises are stated with the same middle word (insect), the conclusion writes itself: keep the subject of the second premise, keep the property of the first, and drop the middle word.
5.G.B.3Look For A PatternWorking backwards, (2) yields the missing premise.
Working backwards is easier here than guessing, because the skeleton has only three slots: if you know which two are filled, the third is not a choice, it is forced.
5.G.B.3Work BackwardsTake care not to reverse the 'all' statement.
The nested circles show the asymmetry at a glance: the small circle is inside the big one, never the other way round, so the two sentences are genuinely different claims.
5.G.B.4Draw A Venn DiagramReading both through, each holds up.
Reading the finished argument aloud and checking that the middle word cancels is a reliable one-pass test, the same way you check a subtraction by adding back.
3.G.A.1Look For A PatternDraw the group as a circle inside the property circle and the one thing as a dot inside the group — then the conclusion is just where the dot has to be.