Which of the following is a subset of the whole numbers?
Greetings, Whole numbers are 0, 1, 2, ... To be a subset the members must also be members of the whole numbers 1. is not a subset , it has the member -1 2. is a subset 3. is not a subset, negative numbers 4. is a subset Regards
Which one of the following is NOT a subset of the set of rational numbers?
whole numbers = 0,1,2,3,4,... integers = ...,-3,-2,-1,0,1,2,3,... natural numbers = 1,2,3,4,5,... (also called counting numbers) rational numbers = fractions of integers (e.g., -2/3 or 1/2 but NOT sqrt(2)/5 or some such) irrational numbers are all numbers that are not rational. a subset is something less than the original set, so in this case only C is not a subset, since A,B,and D are all subsets.
Determine whether the following subsets of C2 (R) are vector spaces or not?
say f1 and f2 both satisfy f(1) = f(2) + 1. Then we need to check their sum. f1+f2 = f1(2)+f2(2)+1+1 =(f1+f2)(2)+2 which is not in the space, so (a) can't be a subspace of C2 (R). b also can't be a subspace but this time it is the scalar multiplication axiom that is being violated. Say f(1)=f(2), then look at f(a1) specifically when a=2. Then f(a1)=f(2)=f(1) <> 2f(1). So (b) is also not a subspace.
If m is a positive integer, which of the following is NOT equal to (2^4)^m?
C. all i did was put in some value for m to see what happens. you could have easily done the same.
Which of the following does not represent the set of integers divisible by 4 from 1 to 40?
way too many and the page is too long. Next time edit it first. 1d 2d .
The no. of subsets S of {1,2,3-----10} with the property :?
Hi ankur, You can reduce this problem relatively simply. Your condition is that integers a,c ∈ S , where S ⊂ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and that integer b ∉ S. I will assume that a ≠ c, (otherwise the solution will be 1023, which is not on the list). However, since S is finite, #(S) ≤ 10, you can always find an integer b such that b ∉ S. Consider b = 20, for example; this will not be in any subset S. So, it suffices to find the number of subsets S containing at least 2 integers. Since the set only contains integers, it suffices to find the number of subsets S with #(S) ≥ 2. The total number of subsets of the original set can be found by summing the binomial coefficients for n = 10: = 10 nCr 0 + 10 nCr 1 + 10 nCr 2 + 10 nCr 3 + 10 nCr 4 + 10 nCr 5 + 10 nCr 6 + 10 nCr 7 + 10 nCr 8 + 10 nCr 9 + 10nCr 10. = 1 + 10 + 45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 + 1. = 1024. How many of these subsets will have less than 2 elements? In fact this is easily seen. 10 nCr 0 is the number of subsets S with 0 elements. That is 10 nCr 0 = 1, so there is one subset with 0 elements. This is obvious, because it is the empty set, Ø. 10 nCr 1 is the number of subsets S with 1 element. That is 10 nCr 1 = 10, so there are ten subsets with 1 element. This is also intuitive, they are: {1} , {2} , {3} , {4} , {5} , {6} , {7} , {8} , {9} , {10}. So, the total number of subsets S with more than one element is: 1024 - 10 - 1 = 1013. ----- Solution: (d) 1013. -----