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Let B[1...n] be an array of integers. To express that no integer occurs twice in the...

Let B[1...n] be an array of integers. To express that no integer occurs twice in the B We may write? (check all the answers that apply)

a) forall i 1..n forall j in 1...n B[i] != B[j]

b)for all i in 1...n forall j in 1...n, i != j => B[i] !=B[j]

c)forll i in 1...n forall j in 1...n i != j and B[i] != B[j]

d)forall i in 1...n forall j in 1...n B[i] =B[j] => i=j

e)forall i in 1...n-1 B[i] != B[i+1]

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Answer #1

b)for all i in 1...n forall j in 1...n, i != j => B[i] !=B[j]

c)forll i in 1...n forall j in 1...n i != j and B[i] != B[j]

d)forall i in 1...n forall j in 1...n B[i] =B[j] => i=j

Explanation: to say that an integer at position i is not repeated again we have to check at every position from 1 to n other than i such that none of the integers at these positions should be equal to the integer at i. This should be checked for all positions from 1 to n to say that no integer occurs twice.

Why not a) forall i 1..n forall j in 1...n B[i] != B[j] ?

This will compare an integer at position i with itself and gives wring result

why not e)forall i in 1...n-1 B[i] != B[i+1] ?

This will check adjacent elements only.

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