Answer with explanation:
Number of People in the group =10 People
The combination between two people is that, they can be either friends or enemies.
Total number of Possible Relation
=18 +16+14+12+10+8+6+4+2
= 90 Relations in all.
Out of 90 relations , 45 will be friends and 45 will be enemies.
⇒Now, we have to prove that, between 10 people, there are either three mutual friends or four mutual enemies, and there are either three mutual enemies or four mutual friends.
→→If there are three mutual friends, total number of people in the group =3 ×2=6 people in the group
And, four mutual enemies in a group means there are 2 people in each group.
So, total number of people if we combine the two groups in which there are either three mutual friends or four mutual enemies
=6 +4
=10
Hence proved.
→→→→Second part is ,in this group there can be either three mutual enemies or four mutual friends.
⇒If there are three mutual enemies, total number of people in the group =3 ×2=6 people in the group
And, four mutual friends in a group means there are 2 people in each group.
So, total number of people if we combine the two groups in which there are either three mutual enemies or four mutual enemies
=6 +4
=10
Hence proved.
= 
= 7/4