Show every subsequence of a subsequence of a given sequence is itselfa subsequence of the given sequence. Hint: Define subsequences asin (3) of Definition 11.1 g

Suppose that ,   and are all sequences, also suppose that   ⊂ ⊂  ∀ ∈ . This implies that ⊂ as required. 

Step-by-step explanation:

If you suppose that ,   and  are all representing three sequences respectively, and you also suppose that   is a subset (in other words subsequence) of and  is a subset (in other words subsequence) of , where n takes its values from the set of positive integers. We can safely say that is a subsequence of and this can demosnstrated mathematically as follows:

Suppose that ,   and are all sequences, also suppose that   ⊂ ⊂  ∀ ∈ . This implies that ⊂ as required. 

-4

step-by-step explanation:

do 6-10=

if u need it to be negative.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.