Syllabus Unit 2 – Algebra Mathematical Logic Logical Problems: Odd Man Out, Syllogism, Blood Relations & Coding-Decoding

Logical Problems: Odd Man Out, Syllogism, Blood Relations & Coding-Decoding

Master Logical Reasoning for CBSE Class 11 Applied Mathematics: Odd Man Out, Syllogism, Blood Relations, and Coding-Decoding with solved examples.

Odd Man Out and Coding-Decoding

Odd man out involves identifying the element that does not follow the pattern established by the other members of a set. Coding-Decoding uses substitution or shifting rules to transform plain text into ciphertext. For example, if A=1, B=2, then the word 'CAT' becomes 3-1-20.

Position(x) = Alphabet_Index(x) + Shift_Value
Example: Solved Example: Identify the odd one from {2, 9, 28, 65, 124}
Show Step-by-Step Solution

Step 1: Observe the pattern: 2 = 1³+1, 9 = 2³+1, 28 = 3³+1, 65 = 4³+1.
Step 2: Check 124: 5³+1 = 126.
Step 3: Since 124 ≠ 126, it is the odd one.
Answer: 124

Syllogism Logic

Syllogism is a form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion. We use Venn diagrams to represent the inclusion or exclusion of sets. If Set A ⊂ Set B and Set B ⊂ Set C, then Set A ⊂ Set C.

If P ⊆ Q and Q ⊆ R, then P ⊆ R
Example: Solved Example: Given All A are B, All B are C. Is All A are C?
Show Step-by-Step Solution

Step 1: Represent A ⊆ B and B ⊆ C.
Step 2: By transitive property of subsets, A ⊆ C.
Answer: Yes, the conclusion is valid.

Blood Relations

Blood relations problems map family hierarchies using symbols or diagrams. We denote males as (+) and females as (-). For instance, if X is the father of Y, then X is one generation above Y.

Generation(Child) = Generation(Parent) - 1
Example: Solved Example: If A is the father of B, and B is the sister of C, how is A related to C?
Show Step-by-Step Solution

Step 1: A is father of B (+).
Step 2: B is sister of C (-).
Step 3: Since B and C are siblings, A is also the father of C.
Answer: Father