Q: Does "The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z {0}, ), see above." provide a valid answer to "What type of numbers under addition form a monoid?"?
OPTIONS:
- yes
- no
A: yes

Q: Does "Macrobius says that Virgil's father was of a humble background; however, scholars generally believe that Virgil was from an equestrian landowning family which could afford to give him an education." provide a valid answer to "Does Macrobius believe Virgil's father came from a distinguished or humble background?"?
OPTIONS:
- yes
- no
A: yes

Q: Does "Dogs may have as many as 300 million odour receptors in their nose, while humans may have only 5 million." provide a valid answer to "How much larger is a dog's olfactory cortex than a person's?"?
OPTIONS:
- yes
- no
A: no

Q: Does "For example, torture was abolished in Prussia in 1740, slavery in Britain in 1834 and in the United States in 1865 (William Wilberforce, Harriet Beecher Stowe, Abraham Lincoln - against Southern Protestants)." provide a valid answer to "When did Prussia stop torture?"?
OPTIONS:
- yes
- no
A:
yes