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Validating a WFF using Resolution

Learn how to prove the validity of a well-formed formula (WFF) using resolution. Also, understand why it may be challenging for some individuals to solve such problems.

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Validating a WFF using Resolution

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  1. Prove that the following wff is valid by means of resolution: xp(x)v xq(x) xp(x)vq(x) Why can’t you do this problem?

  2. You cannot do these problems because you do not know the math between what you now know and what you would need to know to do the problem!

  3. You will have the same problem with understanding the process that scientists call the big bang. Just because you cannot understand some of what scientists say about the big bang does not mean that scientists do not understand it clearly! They know the science between what you know and what is needed to be known to understand the big bang!

  4. The Big Bang Theory

  5. Think of crime scene investigations! Did the detectives see the explosion? No! They have to figure it out from evidence!

  6. That is what astronomers do! They take evidence from space to figure out the science!

  7. Edwin Hubble discovered that the universe is expanding.

  8. If the Universe is expanding, at some time it must have been concentrated in a single point.

  9. Some sort of “event” occurred to cause the change that formed the universe we have today.

  10. This event is what scientists call the "The Big Bang"

  11. Not like an explosion where debris flies off into space!

  12. Instead, it was the expansion of space and time itself, and therefore occurred everywhere at the same time.

  13. Any galaxies farther than ~ 13.7 billion ly away we cannot see! Why: because the light hasn’t had time to get here!!!

  14. Are there galaxies beyond what we can see? Astronomers think that answer is yes. We just can’t see them.

  15. What evidence do we have supporting the Big Bang?

  16. Universal red shift is the evidence for this expansion.

  17. Red shift is is a form of the Doppler Effect. Sound shows Doppler effect too! Clip on this picture to experience the Doppler effect.

  18. red shift What you just heard was the Doppler effect with sound. Red shift is the Doppler effect with light.

  19. Notice that the line groupings are the same – only shifted red.

  20. From our position in the universe, it looks like we are the center because everything appears to be moving away from us. But we are not in the center.

  21. As a balloon gets larger every point moves away from every other point.

  22. If your galaxy was a raisin, notice that every raisin is moving away from every other raisin. In fact, a raisin far away from you is moving away faster than those that are closer. Our expanding universe acts the same way.

  23. The second evidence is Cosmic Microwave Background Radiation!

  24. This is energy “left over” from the Big Bang. -discovered in the early 1960’s.

  25. This is like an oven that was used to make cookies. The cookies are not visible but the smell is there (evidence) and when you open the oven door there is just a little bit of heat still there (another piece of evidence).

  26. What are the two pieces of evidence that support eh Big Bang Theory that we discussed? Video clip of the big bang

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