  Question

Find, which of the following sets are empty: (i)The set of points of intersection of two parallel lines. (ii) A={x:x∈N and 5< x≤6} (iii) B={x:x2+4=0,x∈N} (iv)C={even numbers between 6&10} (v) D={prime numbers between 7&11} Note : The set, which has no element in it, is called the empty or null set.

Solution

(i)"The set of points of intersection of two parallel lines" is an empty set because two parallel lines do not intersect anywhere. Ans. (ii)A={x:x∈N and 5< x≤6}As 5<x≤ 6∴ x=6∴ A={6}Hence given set A is not an empty set. Ans.(iii){x:x2+4=0,x∈N}x2+4=0⇒ x2+4=0⇒ x2=−4⇒x=√−4  which is not a natural number.{even numbers between 6&10}But x ∈ N∴   B={}∴   Given set B is an empty set. Ans. (iv) C={Even numbers between 6  and  10}∴  C={8}Hence it is an empty set. Ans. (v) D={prime numbers between 7&11}Because there is no prime number between 7~and~11.∴   D={} MathematicsConcise MathematicsStandard VIII

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