Use Venn diagrams to check the validity of the argument.

All bachelors are handsome.
Some bachelors do not drink lemonade.
Therefore, some handsome men do not drink lemonade. 1 ---Select--- valid not valid

All squares are rectangles.
All rectangles are polygons.
Therefore, all squares are polygons. 2 ---Select--- valid not valid

No politicians are honest.
Some dishonest people are found out.
Therefore, some politicians are found out.

To check the validity of the arguments using Venn diagrams, we need to represent the relationships between the given statements visually.

Argument 1:

Statement 1: All bachelors are handsome.
We can represent this statement using two overlapping circles. One circle represents the set of bachelors, and the other represents the set of handsome individuals. The entire set of bachelors is included within the set of handsome individuals.

Statement 2: Some bachelors do not drink lemonade.
We can represent this statement with a shaded region within the circle representing bachelors. This shaded region indicates that there is at least one bachelor who does not drink lemonade.

Conclusion: Some handsome men do not drink lemonade.
To verify this conclusion, we need to check if there is any overlap between the shaded region representing bachelors who don't drink lemonade and the circle representing handsome men. If there is an overlap, it supports the conclusion. If there is no overlap, the conclusion is not valid.

Argument 2:

Statement 1: All squares are rectangles.
We can represent this statement using two nested circles. The larger circle represents the set of rectangles, and the smaller circle within it represents the set of squares. Since all squares are rectangles, the circle representing squares is entirely within the circle representing rectangles.

Statement 2: All rectangles are polygons.
We can represent this statement using two nested circles. The larger circle represents the set of polygons, and the smaller circle within it represents the set of rectangles. Since all rectangles are polygons, the circle representing rectangles is entirely within the circle representing polygons.

Conclusion: All squares are polygons.
To verify this conclusion, we need to check if the circle representing squares is entirely within the circle representing polygons. If it is, it supports the conclusion. If there is any region outside the circle representing polygons, the conclusion is not valid.

Argument 3:

Statement 1: No politicians are honest.
We can represent this statement using two non-overlapping circles. One circle represents the set of politicians, and the other represents the set of honest individuals. There should be no overlap between these circles to represent that no politician is honest.

Statement 2: Some dishonest people are found out.
We can represent this statement with a shaded region outside the circle representing honest individuals. This shaded region indicates that there is at least one dishonest person who gets found out.

Conclusion: Some politicians are found out.
To verify this conclusion, we need to check if there is any overlap between the shaded region representing found out individuals and the circle representing politicians. If there is an overlap, it supports the conclusion. If there is no overlap, the conclusion is not valid.