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This is an other interesting question. Be carefull about the statement of question "All non prime number are composite-number" Here we have to understand about Prime Number, Composite Number and Non Prime Number
A number is greater than 1 is called a prime number, if it has only two factors, 1 and the number itself i.e 2, 3, 5, 7, 11 ... also notice that prime number are start form 2.
"A number that can be divided exactly by numbers other than 1 or itself is called a composite number" i.e 4, 6, 8, 9, 10... notice that 1 is not included in composite number and 2, 3 are in prime number list therefore composite number are starting from 4.
Non Prime number
Non prime numbers are the integers that are not prime numbers, i.e. zero (0), One (1), All Composite numbers
All negative integers (-1, -2, -3, -4, ....) are also non prime number.
Therefore all non prime number (specially 0, 1, negative integers etc) are not composite-numbers. And above statement is false.