Problem 4. (10 Marks) Suppose

\\\\Gamma

is a set of formulae, and

A,B

and

C

are formulae. Do not use full truth tables (use only the definitions).\ (a) Prove that if

\\\\Gamma |

|

==_(taut )A->B

and

\\\\Gamma |

|

==_(taut )B->C

then

\\\\Gamma |

|

==_(taut )A->C

.\ (b) Assume

\\\\Gamma |

|

==_(taut )AvvB

. Is it true that

\\\\Gamma |

|

==_(taut )A

or

\\\\Gamma |

|

==_(taut )B

? Prove your answer.

Problem 4. (10 Marks) Suppose is a set of formulae, and A,B and C are formulae. Do not use full truth tables (use only the definitions). (a) Prove that if tautAB and tautBC then tautAC. (b) Assume tautAB. Is it true that tautA or tautB ? Prove your answer. Problem 4. (10 Marks) Suppose is a set of formulae, and A,B and C are formulae. Do not use full truth tables (use only the definitions). (a) Prove that if tautAB and tautBC then tautAC. (b) Assume tautAB. Is it true that tautA or tautB ? Prove your