Which are true of majorities and pluralities? Select all that apply.

A: A majority is a position held by more than half of a group.

B: A plurality is a position held by more than half of a group.

C:A majority is a position held by less than half of the group but is still the most popular decision.

D: A plurality is held by less than half of the group but is still the most popular position.

A: A majority is a position held by more than half of a group.

C: A majority is a position held by less than half of the group but is still the most popular decision.

D: A plurality is held by less than half of the group but is still the most popular position.

The true statements regarding majorities and pluralities are:

A: A majority is a position held by more than half of a group.
C: A majority is a position held by less than half of the group but is still the most popular decision.
D: A plurality is held by less than half of the group but is still the most popular position.

To determine which statements are true of majorities and pluralities, let's break down the definitions of these terms:

1. Majority: A majority refers to a position or decision that is held by more than half of a group. In other words, it means having over 50% support or agreement within that group.

2. Plurality: A plurality, on the other hand, refers to a position or decision that receives the highest number of votes or support but does not necessarily have more than half of the votes or support. In other words, it means being the most popular option, but not necessarily having majority support.

Now, let's evaluate the given statements:

A: A majority is a position held by more than half of a group.
This statement is true. As explained earlier, a majority indeed refers to a position that is held by more than half of a group.

B: A plurality is a position held by more than half of a group.
This statement is false. As mentioned earlier, a plurality does not necessarily require more than half of the group's support but instead focuses on being the most popular position.

C: A majority is a position held by less than half of the group but is still the most popular decision.
This statement is false. A majority requires more than half of the group's support, so it cannot be held by less than half of the group.

D: A plurality is held by less than half of the group but is still the most popular position.
This statement is true. As mentioned earlier, a plurality is the position that receives the highest number of votes or support, even if it does not have more than half of the votes. Hence, it can be held by less than half of the group but still be the most popular.

Therefore, the correct statements are:

A: A majority is a position held by more than half of a group.
D: A plurality is held by less than half of the group but is still the most popular position.