1. Hidden or Suppressed Premises
A premise which isn’t explicitly stated in the argument but which the argument actually relies on to connect the premises to the conclusion:
P: that power station pollutes the environment
(SP) Things that pollute should be shut down
C: we should therefore, shut it down

2. The Importance of Hidden Premises
P: homosexuality is unnatural
(SP) things which are unnatural are wrong
C: therefore, homosexuality is wrong

3. Validity - Structure The moon is made of cheese
Cheese is made from milk
So the moon is made from milk

4. All bankers are honest and hardworking
Hardworking and honest people deserve bonuses
So all bankers should receive bonuses
The head of M&S is an intelligent person
We should listen to intelligent people
So we should listen to the head of M&S

5. Some popular people make good prime ministers
Jeremy Clarkson is a popular person
So Jeremy Clarkson should be prime minister