Logical Reasoning

Odd Man Out, Syllogism, Blood Relations, Coding-Decoding β€” Applied Maths 11

πŸ” Odd Man Out

Ek group mein se wo item dhundho jo baaki sabse alag hai β€” common pattern dekho!

Step 1: Pehle dekho kya common hai β€” category, shape, number pattern, alphabets Step 2: Jo element match na kare woh odd one out hai
Example 1: 2, 4, 6, 9, 10, 12
Sab even hain except 9 (odd number) β†’ Odd one out = 9
Example 2: Dog, Cat, Cow, Eagle, Horse
Sab domestic animals hain except Eagle (bird) β†’ Odd one out = Eagle
Example 3: 17, 23, 37, 43, 49, 53
Sab prime numbers hain except 49 (= 7Β²) β†’ Odd one out = 49

πŸ’¬ Syllogism

Do ya zyada statements se logical conclusion nikalna. Venn diagrams se solve karo!

Types of statements: All A are B β†’ A βŠ‚ B (circle A fully inside B) Some A are B β†’ A ∩ B β‰  βˆ… (partial overlap) No A is B β†’ A ∩ B = βˆ… (no overlap) Some A are not B β†’ part of A is outside B
Example: All cats are animals. All animals are living things. Conclusion?
All cats are animals β†’ Cats βŠ‚ Animals
All animals are living β†’ Animals βŠ‚ Living
∴ Cats βŠ‚ Living β†’ All cats are living things βœ“
Example: Some birds can fly. Pigeons are birds. Conclusion?
We can't definitely say pigeons can fly (some = not all).
Conclusion: Data inadequate / May or may not be true

πŸ‘¨β€πŸ‘©β€πŸ‘§ Blood Relations

Family tree samjho, relationships trace karo. Common terms yaad raho!

TermMeaningTermMeaning
SiblingBrother/SisterMaternalMother's side
PaternalFather's sideIn-lawBy marriage
Nephew/NieceSibling's childCousinUncle/Aunt's child
Example: A is B's mother. C is A's sister. D is C's son. D is B's _?
A is B's mother β†’ B is A's child
C is A's sister β†’ C is B's aunt (maasi/bua)
D is C's son β†’ D is C's son, C is B's aunt
∴ D is B's cousin

πŸ” Coding-Decoding

Ek pattern se letters/numbers encode hote hain. Pattern dhundho, phir decode karo!

Letter +1 Rule:
A→B, B→C, CAT→DBU
Reverse Alphabet:
A→Z, B→Y, Z→A
Number codes:
A=1,B=2,...,Z=26
Position shift:
+2, -3 etc.
Example: If CHAIR = EJCKT, then TABLE = ?
C+2=E, H+2=J, A+2=C, I+2=K, R+2=T (each letter +2 shift)
T+2=V, A+2=C, B+2=D, L+2=N, E+2=G β†’ VCDNG