document.write( "Question 1173190: Let G ={4x | x ∈ N} H ={y | y is a prime number}
\n" ); document.write( "Find G ∩ H. \n" ); document.write( "

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\n" ); document.write( "Answer: The empty set
\n" ); document.write( "We can denote this as { } which is just a pair of curly braces with nothing inside it. We could also use the special symbol

to denote the empty set.\r
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\n" ); document.write( "Explanation:\r
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\n" ); document.write( "\n" ); document.write( "Set G describes all multiples of 4. So we have: {4,8,12,16,...}
\n" ); document.write( "Set H describes the set of prime numbers: {2,3,5,7,11,...}
\n" ); document.write( "The two sets have nothing in common.\r
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\n" ); document.write( "\n" ); document.write( "Any multiple of 4 will have 4 as a factor. The value 4 itself isn't prime. A prime number only has factors of 1 and itself. For instance, 7 is prime because the only factors of it are 1 and 7.
\n" ); document.write( "So this is why if you select a multiple of 4, then it won't be prime. If you select a prime number, then it won't be a multiple of 4.\r
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\n" ); document.write( "\n" ); document.write( "Because the two sets have nothing in common, their intersection is the empty set.
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