Determine whether the two events are disjoint for a single trial. (hint: consider "disjoint" to be equivalent to "separate" or "not overlapping".)randomly selecting aa trumpettrumpet from the instrumentinstrument assembly line and getting one that is free of defects. randomly selecting aa trumpettrumpet from the instrumentinstrument assembly line and getting one with a dented belldented bell.

The hint is quite helpful; not overlapping is a good way of thinking about disjoint events. First of all, consider the first event. If one picks a trumpet that is free of defects, we have that the trumpet cannot have a dented bell. Similarly, if the trumpet has a dented bell, it cannot be free of defects; thus these events are disjoint since whenever one happens, we can be sure that the other does not. An example of non-disjoing events would be : 1) randomly picking a trumpet with a defect 2) randomly picking a trumpet with a dented bell. In this case, if the second event happens, we will have that the 1st event will also happen, so there is an overlap. A more generic example is the following: 1) randomly picking a tall person 2) randomly picking a brown-haired person. Since there are tall people with brown hair, there is overlap and thus the events are not disjoint.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax   (given)ax ≅ ax (common side)

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)