<p>Let <em>R</em> = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} and <em>A</em> = {1, 2, 3, 4}. The relation <em>R</em> is</p>
Step-by-Step Solution
Key Concept: A relation must be tested against four properties: reflexivity (every element related to itself), symmetry (if (a,b) in R then (b,a) in R), transitivity (if (a,b) and (b,c) in R then (a,c) in R), and whether it's a function (each domain element maps to exactly one range element). Check each systematically.
<p><strong>Step 1: Check Reflexivity</strong></p><p>For reflexivity, we need (1,1), (2,2), (3,3), (4,4) ∈ R. These are missing. ✗ Not reflexive</p><p><strong>Step 2: Check Symmetry</strong></p><p>Check if (a,b) ∈ R ⟹ (b,a) ∈ R:</p><p>• (1,3) ∈ R but (3,1) ∈ R ✓</p><p>• (4,2) ∈ R but (2,4) ∈ R ✓</p><p>• (2,3) ∈ R but (3,2) ∉ R ✗ Not symmetric</p><p><strong>Step 3: Check Transitivity</strong></p><p>Check if (a,b), (b,c) ∈ R ⟹ (a,c) ∈ R:</p><p>• (2,4) ∈ R and (4,2) ∈ R, need (2,2) ∉ R ✗</p><p>• (2,3) ∈ R and (3,1) ∈ R, need (2,1) ∉ R ✗ Not transitive</p><p><strong>Step 4: Check if Function</strong></p><p>Element 2 maps to both 4 and 3. So 2 has two images. ✗ Not a function</p><p>∴ Answer: R is <strong>None of the above standard types</strong> (or just a relation) - Option C</p>
Correct Answer: C