True or false from a picture

In your book, Maths Mela (Chapter 15, Data Through Pictures), page 187 shows a group of schoolchildren. Some wear caps, some wear glasses, some hold books and some carry backpacks. The book gives statements, such as 'more than half of the children are wearing glasses', and asks: true or false? To decide, we count.

Here is a group like that, described in words so you can count. There are 12 children: 7 girls and 5 boys. 5 children wear glasses: 3 girls and 2 boys. 6 children wear caps: 4 girls and 2 boys. Of these, 3 children wear both glasses and a cap: 2 girls and 1 boy. 7 children hold books: 3 girls and 4 boys. 2 children have all three: a cap, a book and a backpack.

Now test the statements. 'All the girls wear glasses': only 3 of the 7 girls do, so false. 'More than half of the children wear glasses': half of 12 is 6, and 5 is less than 6, so false. 'More boys than girls hold books': 4 boys and 3 girls, so true. 'Some children wear both glasses and caps': 3 children do, so true.

Be careful with children who have two things at once. A child with glasses and a cap is counted with the glasses AND with the caps. So 6 cap-wearers take away the 3 who also wear glasses leaves 3 children who wear a cap but no glasses.