Im pretty sure 2 3 and 4 are false but after that Im at a lo

I\'m pretty sure 2, 3, and 4 are false, but after that I\'m at a lost. If one of them is wrong then the whole problem is wrong. Any help will be appreciated. Thanks.

The statement is true. 1. If S is a linearly dependent set, then every element in S can be written as a linear combination of the other elements in S. 2. Any set that does not contain the zero vector is a linearly independent set. 3. A set with more than 1 vector is linearly dependent if and only if for any pair of vectors in the set, at least one of them is a scalar multiple of the other 4. A set with more than 1 vector is linearly independent if and only if for any pair of vectors in the set, neither of them is a scalar multiple of the other 5. Non empty subsets of linearly independent sets are linearly independent sets. 6. Non empty subsets of linearly dependent sets are linearly dependent. 7. Suppose U and V are subsets of a vector space W, and U is contained in V. If U is linearly dependent, then V is linearly dependent. 8. Suppose U and V are subsets of a vector space W, and U is contained in V. If U is linearly independent, then Vis linearly independent. 8. linearly dependent. 0. Suppose U and V are linearly independent subsets of a vector space W. The union of U and V is linearly independent

Solution

In the given statement s 2^nd ,3^rd and 4^th statements are FALSE. And the remaining statements are TRUE.