Question

1. provide counterexamples for the following statements:

if a person is an artist, then they must be a painter.
counterexample: $square$

if a month starts with the letter j, it must be a summer month.
counterexample: $square$

if an angle is acute, it must measure 50 degrees.
counterexample: $square$

Explanation:

1. For the first statement, an artist can work in other mediums like sculpture, so a sculptor is an artist but not a painter.
2. For the second, January begins with "J" but is in winter (Northern Hemisphere), contradicting it being a summer month.
3. For the third, acute angles are any between \(0^\circ\) and \(90^\circ\), so a \(30^\circ\) angle is acute but not \(50^\circ\).

Answer:

1. A person who is an artist could be a sculptor (sculptors are artists but not painters).
2. January starts with "J" but is a winter month (in the Northern Hemisphere), not a summer month.
3. An acute angle measuring 30 degrees (acute angles are between 0 and 90 degrees, so 30 degrees is acute and not 50 degrees).