Question

Write a proof of each of these theorems in English prose.

1) Hypotheses:
If the Pope is here, then the Queen is here.
If the Queen is here, then the Registrar is here.

Conclusion:
If the Pope is here, then the Registrar is here.

2) THEOREM. Assume:
(a) If the Pope is here, then the Registrar is here.
(b) If the Queen is here, then the Spy is here.
(c) The Pope and the Queen are both here.
Then the Registrar and the Spy are both here.

3) THEOREM. Assume:
(a) If Adam is here, then Betty is here.
(b) If Betty is not here, then Charlie is here.
(c) Either Adam is here, or Charlie is not here.
Then Betty is here.

4) THEOREM. Assume:
(a) If Jack and Jill went up the hill, then something will go wrong.
(b) If Jack went up the hill, then Jill went up the hill.
(c) Nothing will go wrong.
Then Jack did not go up the hill.

Answer 1

Solution:

given that

Hypotheses: If the Pope is here, then the Queen is here. If the Queen is here, then the Registrar is here. Conclusion: If the Pope is here, then the Registrar is here

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3.Q 3 Theoher whae 2. 3. P hoata R. 'Jack fr hill 3, (3 A