State whether the following statement are True or False and also give the reason in support of your answer.

a) Collection of intelligent students of IGNOU forms a set.

b) Following rule is a function from A to B

c)  

d) The negation of the following statement p is-p.

p: Longest chord of a circle is diameter -p: Diameter is the shortest chord of circle

e) Any term of an AP(except the first and last) is equal to half the sum of terms which are equidistant from it on both sides

a) False  
   A set is a well-defined collection of distinct objects. The term "intelligent students of IGNOU" is vague and subjective, as intelligence is not objectively measurable in a universally agreed manner. Therefore, this collection is not a well-defined set.  

b) Depends on the given rule  
   The given rule must satisfy the definition of a function: each element of set \( A \) must be assigned to exactly one element of set \( _____ _________ _______ _________ __________.
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