3. Is the formula P → (PVQ) valid in... (a) ...Łukasiewicz's system? (b) ... Kleene's? (c) ...the logic of paradox? (d) ... the system of supervaluations? In each case, justify your answer: if the answer is yes, give a metalogic proof; if the answer is no, give a counterexample.

Given that P(A)=0.3 and P(B)=0.7, answer the following:(please round all numerical answers to four decimal placesa) Assuming that A and B are independent, what is P(A and B)? b) Assuming that A and B are independent, what is P(A or B)? c) Assuming that A and B are independent, what is P(A|B)? d) If we are given that P(A and B) = 0.1, what is P(A|B)?

I don't understand this. Please Helppppp!!!!

Show that (a) if P(A) = P(B) = P(AB), then P(ABUBA) = 0; (b) if P(A) = P(B) = 1, then P(AB) = 1.

I need help with this problem and an explanation for the solution described below (Discrete mathematics):

Suppose that BC financial aid alots a textbook stipend by claiming that the average textbook at BC bookstore costs $ 60.92. You want to test this claim.The null and alternative hypothesis in symbols would be: a) H0:p≤60.92H1:p > 60.92 b) H0:μ=60.92; H1:μ≠60.92 c) H0:μ ≥ 60.92; H1:μ < 60.92 d) H0:μ ≤ 60.92; H1:μ > 60.92 e) H0:p≥60.92; H1:p<60.92 f) H0:p=60.92; H1:p≠60.92 The null hypothesis in words would be: The average price of all textbooks from the store is $$ 60.92 The average price of textbooks in a sample is $$ 60.92 The average of price of all textbooks from the store is less than $$ 60.92. The proportion of all textbooks from the store that are less than 60.92 is equal to 50% The average of price of all textbooks from the store is greater than $$ 60.92. Based on a sample of 110 textbooks at the store, you find an average of 65.72 and a standard deviation of 17.The point estimate is: ______ (to 3 decimals)The 95 % confidence interval (use z*) is: _____ to ______…

Suppose that BC financial aid allots a textbook stipend by claiming that the average textbook at BC bookstore costs $ 79.12. You want to test this claim. The null and alternative hypothesis in symbols would be: O Ho:u 2 79.12 H1:4 79.12 O Ho:p = 79.12 H1:p # 79.12 O Ho:H 79.12 O Ho:p 2 79.12 H1:p < 79.12 O Ho:u = 79.12 H1:µ 7 79.12 The null hypothesis in words would be: OThe average price of all textbooks from the store is $ 79.12 O The average price of textbooks in a sample is $ 79.12 O The average of price of all textbooks from the store is greater than $ 79.12. OThe proportion of all textbooks from the store that are less than 79.12 is equal to 50% OThe average of price of all textbooks from the store is less than $ 79.12. The population standard deviation is known to be 10 and based on a sample of 50 textbooks at the store, you find an average of 93.32. The point estimate is: The 95 % confidence interval is: to (to 3 decimals) Based on this we: O Reject the null hypothesis O Fail…