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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