Question

there are 60 students studying sciences (biology chemistry and physics) 7 study biology, chemistry and physics. 12 study biology and chemistry. 15 study chemisty and physics. 35 study biology 32 study physics. complete the venn diagram.

Answer 1

Explanation:

Draw a three-ring Venn diagram.

7 students study all three subjects, where the three circles overlap.

12 students study biology and chemistry, which includes the 7 who also study physics. So there are 5 who study biology and chemistry but not physics.

Similarly, 15 students study biology and physics, which includes the 7 who also study chemistry. So there are 8 who study biology and physics but not chemistry.

And, 20 students study chemistry and physics, which includes the 7 who also study biology. So there are 13 who study chemistry and physics but not biology.

35 students study biology, which includes the 5 who study chemistry, the 8 who study physics, and the 7 who study both chemistry and physics. Therefore, there are 15 students who study only biology.

Similarly, 32 students study physics, which includes the 8 who study biology, the 13 who study chemistry, and the 7 who study both biology and chemistry. Therefore, there are 4 students who study only physics.

Since there's a total of 60 students, there must be 8 students who study only chemistry.

Answer 2

7 students study all three subjects, where the three circles overlap.

Twelve students—seven of whom also study physics—study chemistry and biology. Thus, five of them focus on chemistry and biology but not physics.

In a similar vein, seven students who study chemistry are among the fifteen students who study physics and biology. Eight of them study physics and biology but not chemistry.

Additionally, 20 students—including the seven who study biology—learn physics and chemistry. Thirteen of them study physics and chemistry but not biology.

Of the 35 students, five study chemistry, eight study physics, and seven study both chemistry and physics. The remaining students study biology. As a result, fifteen students focus exclusively on biology.

Comparably, 32 students—eight of whom study biology, thirteen of whom study chemistry, and seven of whom study both biology and chemistry—learn physics. As a result, four pupils focus solely on physics.

There must be eight pupils studying chemistry alone out of the total of 60.