Natural Deduction Practice Problems

Here are two natural deduction practice problems I wrote to prepare myself for last semester’s logic final. They can be solved in about 5-10 steps. Feel free to comment with your solutions. The first person to correctly answer will not receive a prize because I’m not Oprah.

Prove “p” given:

  1. p v ~q                  
  2. a–>q                   
  3. ~s–>~b              
  4. [~a-->b] & ~s     

Prove “p” given:

  1. p v ~q                  
  2. s & t                     
  3. ~[~q & t]            

Regards,

Charles Bonaventure


Poem: Character Sketch

empty bar

(Photo credit: massdistraction)

My lover’s eyes work hard for double pay

catching dreams by night

and sunbeams by day

.

Her jubilant voice, like two at a waltz,

Sounds happy and free

Embracing the schmaltz

.

And it’s no lie to say, her precious locks

are decrescendos

cascading upon rocks

-CB


Poem: Cold February

Bench

Bench (Photo credit: griangrafanna)

Walking

my silent eyes reached out

to touch her

Her eyes full of laughter

sacred, eternal

A grasp on my arm

her eyes said in return

.

Hearing silent stories

pains, joys, dreams

humanity

in my heart

that moment never ended

 .

walking

as I was

aware now

that I’m walking

away

-CB


Poem: Rushing

Stream

I am the one who hides in springs to dance among the pines

My forgotten streams fill your dreams, my currents flow in time

Marked by forty bridges, moving softly with currents ethereal

My churning body has no form, only my weight is material

I drain the countryside, marked-up ordered grids in rows

I bring health to your fields, trickling, tumbling from your hose

Bound, blockaded, burdened, I am held down by levies wide

Sometimes shackled at the wrists as the floods of my fury preside

I wash myself down valleys carved and cut by strength I contain

To bubble underneath a footbridge that crosses 15th Street and Main

Casting arms outward, I hold three hundred fathoms with my brawn

While once you found me narrow, tremble now as I stretch and yawn

I form the plains as I go, reaching towards the heaving tide

I open my fruits to the delta, kissing the ocean, where I subside

.

-C.B.


Feelings are unspoken words

English: Lonely green tree in Kurdistan provin...

(Photo credit: Wikipedia)

So it ended up that last Tuesday I felt like a post-it note

Because I’m ignored most when I’m in view

Just last month I was the victim of a victimless crime

Because I shouldn’t really exist but I still do

And every day I feel like I’m older than time

Because I can’t remember my birth

And every third day I feel like a computer

Now that doesn’t make much sense

When everything in life is forgotten

I just feel

-Charles Bonaventure


Poem: headlights

On the top of the mountain I saw no stars

upon the world, only headlights and cars

streaming through a world of dark shadows

scaring a land that is haunted and hallowed

a lonely metropolis where a million dwell

in towers of brick reaching up to the skies

a living forest fashioned with beams of steel

that twinkle as if to say bye and goodbye

how happy would I be if these clouds were gone

but tonight there’s no heaven, only this hell

then nothing would keep nature’s beauty withdrawn

on the top of the mountain, my heart knows well


Poem: Until that Time

Great Sand Sea of Egypt.

(Photo credit: Wikipedia)

Until the stars are bright as day

so the darkness fades away

Until cracked dirt is made fertile

when the clouds are squeezed empty

Until the seas are commanded calm

and all will find them fragile as glass

Until nature’s perfume fills my mind’s eye

so that  it is intoxicated with beauty

Until my fear is abated

so all violence is hated

Until the song of hope plays

for the last moment of grace

Until the sky and the earth love

until they are tired with passion

Until up is down and down is left

leaving my vision blurred

 I will write a song

-Charles Bonaventure


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