Syllogisms (Deductive Logic)
Nick Featherstone
Teacher
Introduction - Syllogisms
What are Syllogisms?
A short paragraph or a set of statements.
Using the given information, you must deduce if a set of statements follow logically from the passage.
E.g.
All Bops have either feathers or fur and are either Cocos or Pips.
Most Cocos have blue fur but all other Cocos, as well as all of the Pips, have red fur.
Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does not follow.
All blue Cocos have fur. - Yes
Any red Bop must be a Pip. - No
Some Pips with fur are coloured blue. - No
None of the blue Bops have feathers. - Yes
More Bops have feathers than fur. - No
Why are Syllogisms used in the UCAT?
Assesses your ability to interpret information and identify assumptions from statements.
Enhances your ability to avoid assumptions not supported by evidence.
Explainer Video
Filmed by our Maths department, this video walks through how to solve Syllogisms efficiently from first principles.
Worked Examples
Question 1 – Easy
All the people who live in a flat, except Emily, like apple juice. More than one person in the house likes orange juice.
Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does not follow.
Emily likes orange juice. - No
If a person in the flat does not like orange juice, they must like apple juice. - No
If a person in the flat does not like apple juice, it must be Emily. - Yes
If only two people in the flat like orange juice, one must be Emily. - No
Someone in the flat likes orange juice and apple juice. - Yes
Worked Solution
Draw diagrams to represent each of the statements in the question, using the first letter(s) of each category to save time.
‘All the people who live in a flat, except Emily, like apple juice.’
‘More than one person in the house likes orange juice.’
E.g.
E = Emily A = Apple juice O = orange juice
100% people except E like A
> 1 like O
Referring to your diagrams, work through each of the statements.
1st conclusion – Does not follow as there is no information on whether she likes orange juice.
2nd conclusion – Does not follow as it could be Emily that does not like orange juice, and we know she does not like apple juice.
3rd conclusion – Does follow as all those that live in the flat like apple juice except for Emily.
4th conclusion – Does not follow as there is nothing to suggest Emily likes orange juice, so although it could be Emily, it could also be another person in the house.
5th conclusion – Does follow as more than one person in the house likes orange juice and only Emily does not like apple juice, so at least one person must like apple juice and orange juice.
Question 2 – Medium
All students from a Primary School received a gold star in Biology and no student in the Primary School received a silver star in Chemistry. The Secondary School only admits students if they have a gold star in Chemistry.
Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does not follow.
Billy studied at the Primary School before moving to Secondary School so he must have received a gold star in both Biology and Chemistry. - Yes
The Secondary School does not offer the subject Biology. - No
As Mathew attended Primary School he did not obtain a silver star. - No
No Primary School student can be admitted to Secondary School. - No
Sarah received a silver star in Chemistry so she did not attend Secondary School. - Yes
Worked Solution
Draw diagrams to represent the information given in the question stem, to save time rereading the question stem when answering the statements.
Write the first letter of each ‘category’ to save time.
Draw diagrams for each of the following statements as follows:
‘All students from a Primary School received a gold star in Biology’
‘No student in the Primary School received a silver star in Chemistry’
‘The Secondary School only admits students if they have a gold star in Chemistry.’
E.g.
G = gold star S = Silver star B = Biology C = Chemistry
SS = secondary school
100% = G → B
0% students = S → C
SS → only if G → C
Work through each of the statements using the diagrams you have drawn.
1st conclusion - Does follow because the Secondary School admits only if they have a gold star in Chemistry.
SS → only if G → C
2nd conclusion - Does not follow because there is no reference to Biology being offered as a subject at Secondary School.
3rd conclusion - Does not follow because we are only told that no student received a gold star in Chemistry but nothing about the other subjects.
4th conclusion - Does not follow because the Secondary School admits students who received a gold star in Chemistry.
5th conclusion - Does follow because no Secondary School student got a silver star in Chemistry.
Question 3 - Hard
All aspects of a business are either controllable or uncontrollable but none of the uncontrollable aspects of the business are related to sales or marketing. Employee satisfaction is a controllable aspect of the business.
Place ‘Yes’ if the conclusion does follow. Place ‘No’ if the conclusion does not follow.
Some aspects of the business are controllable. - Yes
Employee satisfaction is the only controllable aspect of the business. - No
All aspects of the business related to sales or marketing are uncontrollable. - No
All uncontrollable aspects of the business are related to neither sales nor marketing. - Yes
Not all controllable aspects of the business are related to sales and marketing. - Yes
Worked Solution
Draw diagrams to represent the information given in the question stem, to save time rereading the question stem when answering the statements.
Write the first letter of each ‘category’ to save time.
Draw diagrams for each of the following statements as follows:
‘All aspects of a business are either controllable or uncontrollable’
‘none of the uncontrollable aspects of the business are related to sales or marketing’
‘Employee satisfaction is a controllable aspect of the business.’
E.g.
C = controllable U = uncontrollable S = sales M = marketing E = employees
:) = satisfaction
0% US/M
E :) = C
Work through each of the statements using the diagrams you have drawn.
1st conclusion – Does follow because we are told that sales, marketing and employee satisfaction are controllable aspects of the business.
2nd conclusion – Does not follow because we are told that employee satisfaction is one controllable aspect of the business; there is no information that it is the only controllable aspect of the business.
3rd conclusion – Does not follow because the passage states that sales and marketing are not uncontrollable, therefore they must be controllable aspects of the business.
4th conclusion – Does follow because none of the uncontrollable aspects are related to sales and marketing.
5th conclusion – Does follow because employee satisfaction is stated as a controllable aspect of the business.
Worked Examples Video