To answer this question, the very first thing we observe is that each statement implies itself.
So we will draw every element of the diagonal as true.
We also observe that "not pink" implies "green" is the same as pink or green.
If you do the truth table, you find that this is true either if green is true, which will be the case of B as well,
or if pink is true, in which case the precondition which is implied will be false, and therefore the entire statement is true.
So we can find out that B is exactly the same as D.
With that in mind, we answer the question for A to C first.
Pink clearly implies that pink or green is true. It doesn't imply that pink and green is true, so C is not open.
But because B is equivalent to D, we also check over here.
Pink or green doesn't imply pink, because green might be true, and doesn't imply pink and green because green might be false.
But it does imply D because D is exactly the same as B.
Pink and green implies pink. It also implies pink or green.
And since B is the same as D, implies D.
And finally, for this one over here, we just copy over B. So we get this guy and this guy over here.
最初にそれぞれの命題が 自身を含意することが分かるので
対角線上のすべての要素が真となります
真理値表では“ピンクでないならば緑”は “ピンクまたは緑”と同じだと分かります
緑が真ならDは真です Bについても真となります
もしピンクが真なら必要条件が偽となるので 全体の命題は真となります
よってBがDとまったく同じだと いうことが分かります
これを頭に入れて Aから順に答えていきましょう
ピンクは“ピンクまたは緑”を含意しますが “ピンクかつ緑”を含意しないのでCは偽です
BはDと同じなのでここにもチェックを入れます
“ピンクまたは緑”はピンクを含意しません 緑が真でピンクが偽であるかもしれないからです
“ピンクかつ緑”は緑が偽かもしれません しかしDはBと同じなのでBならばDです
“ピンクかつ緑”はピンクを含意し “ピンクまたは緑”も含意します
そしてBはDと同じなのでDも成立します
最後はここBから単純にコピーすればいいので こことことにチェックが入ります