&In and &Out The rules for & are very simple. A A&B A&B

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Presentation transcript:

&In and &Out The rules for & are very simple. A A&B A&B B A &Out B &Out A&B &In

&In and &Out The strategies are simple too: If you have a sentence with the shape A&B, then use &Out to obtain A and B. 1. P&(Q&R)

&In and &Out The strategies are simple too: If you have a sentence with the shape A&B, then use &Out to obtain A and B. 1. P&(Q&R) 2. P 1 &O 3. Q&R 1 &O

&In and &Out The strategies are simple too: If a sentence with the shape A&B is your goal, prove A and prove B and join them together with &In. (P&Q)&R GOAL

&In and &Out The strategies are simple too: If a sentence with the shape A&B is your goal, prove A and prove B and join them together with &In. P&Q GOAL R GOAL (P&Q)&R &I

&In and &Out 1) P&((P&Q)>R) A 2) Q A R GOAL

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O R GOAL

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O R GOAL

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O P&Q GOAL R 4,? >O

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O P&Q GOAL R 4,5 >O

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O P&Q ?,? &I R 4,5 >O

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O 5) P&Q 3,2 &I 6) R 4,5 >O

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O R GOAL

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O R GOAL

&In and &Out 1) P&((P&Q)>R) A 2) Q A 3) P 1 &O 4) (P&Q)>R 1 &O P&Q GOAL R 4,? >O

Do not confuse &Out with >Out &In and &Out Do not confuse &Out with >Out 1) P>Q 2) P 1 >O WRONG

For more click here &In and &Out Do not confuse &Out with >Out 1) P>Q 2) P 1 >O WRONG A A>B B >O For more click here