Distant planet?

Question

In a distant planet, there are four forms of life beings: zadohs, pugwigs, kahoots and zingzags.

All zadohs are pugwigs. Some pugwigs are kahoots. All kahoots are zingzags.

Which of the following statements must necessarily be true?

1. Some zadohs are zingzags

2. Some kahoots are zadohs

3. All kahoots are pugwigs

4. Some zingzags are pugwigs

5. All zingzags are zadohs

6. Some zadohs are kahoots

Answer 1

some zingzags are pugwigs

Answer 2

Only statement 4 has to be true:

Draw a small circle. Label it zadohs. Around this circle, draw another larger circle that completely surrounds the zadohs. Label this circle pugwigs.

Now draw another circle that contains part of the pugwigs but does not contain any of the zadohs circle. These are the kahoots. Color the shared pugwigs/kahoots area with a highlighter.

Lastly, draw a circle that contains all of the kahoots circle, but none of the zadohs circle. These are the zingzags

You've satisfied all the conditions. Now go down the list of statements.

Statements 1, 2, 3, 5, and 6 are clearly false for your drawing.

Statement 4 is true. The highlighted area contains the life forms that are pugwigs, kahoots, and zingzags at the same time

You cannot draw a diagram using the given conditions where statement 4 is false.

Answer 3

i'd say 4

Answer 4

4

The way I did it, which may not be the proper way to do it, was to draw circles.

1) Draw a small circle called "Zad"

2) Draw a circle that completely surrounds zad and call it "Pug"

3) Draw a circle that shares some of Pug's area (but not necessarily any of Zad's) and call it "Kah"

4) Draw a circle that completely surrounds Kah and call it "Zing".  

You'll see that Zing necessarily shares some of Pug's area, but not necessarily any of Zad's.