Here we show that two problems are in NP: Clique (given graph G and integer k, and determine whether G has a k-clique), and Subset Sum (given a set of integers S and target sum t, and determine if a subset of S sums to t). We show that these are true by using certificates for each.<br /><br />Easy Theory Website: <a href="https://www.easytheory.org" target="_blank" rel="nofollow">https://www.easytheory.org</a><br />Become a member: <a href="https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join" target="_blank" rel="nofollow">https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join</a><br />Donation (appears on streams): <a href="https://streamlabs.com/easytheory1/tip" target="_blank" rel="nofollow">https://streamlabs.com/easytheory1/tip</a><br />Paypal: <a href="https://paypal.me/easytheory" target="_blank" rel="nofollow">https://paypal.me/easytheory</a><br />Patreon: <a href="https://www.patreon.com/easytheory" target="_blank" rel="nofollow">https://www.patreon.com/easytheory</a><br />Discord: <a href="https://discord.gg/SD4U3hs" target="_blank" rel="nofollow">https://discord.gg/SD4U3hs</a><br /><br />Youtube Live Streaming (Sundays) - subscribe for when these occur.<br /><br />Merch:<br />Language Hierarchy Apparel: <a href="https://teespring.com/language-hierarchy?pid=2&cid=2122" target="_blank" rel="nofollow">https://teespring.com/language-hierarchy?pid=2&cid=2122</a><br />Pumping Lemma Apparel: <a href="https://teespring.com/pumping-lemma-for-regular-lang" target="_blank" rel="nofollow">https://teespring.com/pumping-lemma-for-regular-lang</a><br /><br />If you like this content, please consider subscribing to my channel: <a href="https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1" target="_blank" rel="nofollow">https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1</a><br /><br />▶SEND ME THEORY QUESTIONS◀<br />[email protected]<br /><br />▶ABOUT ME◀<br />I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.<br />...<br /><a href="https://www.youtube.com/watch?v=NYfH3c4FY3Y" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=NYfH3c4FY3Y</a>