Logical Reasoning · Unit 3
Logical Deductions: MDCAT Notes and MCQs
Logical deduction asks which conclusion must follow from given statements — use only the information provided.
Syllogisms — use Venn diagrams
| Statements | Valid conclusion |
|---|
| All A are B; All B are C | All A are C |
| All A are B; No B is C | No A is C |
| Some A are B; All B are C | Some A are C |
| Some A are B; No B is C | Some A are not C |
| All A are B; Some B are C | No definite conclusion about A and C |
Two "some" or two negative premises → no definite conclusion. "All A are B" → "Some B are A" is valid (conversion), but "All B are A" is not.
Blood relations
Draw a family tree: use + / − for male/female, horizontal line for siblings, vertical for generations. Father's/mother's mother = grandmother; "only son of my grandfather" = my father.
Direction sense
Draw a compass. Facing north: right = east, left = west. Facing south: right = west. Use Pythagoras for shortest distance.
Ranking & ordering
Total = rank from top + rank from bottom − 1. For seating/ordering, draw the arrangement and place the most definite clues first.
PMDC learning outcomes for this unit
- Deductions: 5.3.1 Predict new relations on the basis of given relations.
- Deductions: 5.3.2 Develop new structure on the basis of information in already drawn structures.
Q1
All doctors are graduates. All graduates are literate. Which conclusion follows?
AAll literate people are doctors
BAll doctors are literate
CNo literate person is a doctor
DSome graduates are not doctors
Show answer
Answer: B (All doctors are literate). All A are B, all B are C → all A are C.
Q2
All roses are flowers. Some flowers fade quickly. Which conclusion definitely follows?
ASome roses fade quickly
BAll roses fade quickly
CNo rose fades quickly
DNone of these definitely follows
Show answer
Answer: D (None of these definitely follows). The fading flowers may or may not include roses.
Q3
Some cats are pets. No pet is wild. Which conclusion follows?
AAll cats are wild
BSome wild animals are cats
CNo cat is wild
DSome cats are not wild
Show answer
Answer: D (Some cats are not wild). Some A are B and no B is C → some A are not C.
Q4
A is B's brother. C is A's father. D is C's mother. How is D related to B?
AAunt
BMother
CSister
DGrandmother
Show answer
Answer: D (Grandmother). C is the father of A and B; D is C's mother → B's grandmother.
Q5
Pointing to a boy, Sara said, 'He is the son of my grandfather's only son.' The boy is Sara's:
ANephew
BUncle
CBrother
DCousin
Show answer
Answer: C (Brother). Grandfather's only son is Sara's father, so the boy is her brother.
Q6
Ali walks 5 km north, turns right and walks 3 km, then turns right and walks 5 km. Where is he from the start?
A3 km east
B5 km south
C8 km east
D3 km west
Show answer
Answer: A (3 km east). North 5, east 3, south 5 → net 3 km east.
Q7
In a class of 40 students, Hina is 12th from the top. What is her rank from the bottom?
Show answer
Answer: C (29th). 40 − 12 + 1 = 29.