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| 1. |
If R and R′ are symmetric relation (not disjoint) on a set A, then the relation R ∩ R′ is(1) reflexive(2) symmetric(3) transitive(4) none of these |
| Answer» <p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif"><strong>Correct option (2) symmetric</strong></span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif"><strong>Explanation: </strong></span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">(x, y) ∈ R ∩ R′</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">⇒ (x, y) ∈ R and (x, y) ∈ R′</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">⇒ (y, x) ∈ R and (y, x) ∈ R′</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">since R and R′ are symmetric. </span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">⇒ (y, x) ∈ R ∩ R′</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">⇒ R ∩ R′ is symmetric.</span></span></p> | |